If you were obscenely rich and had obtained the rights to the Mass Effect franchise what would you d

This lacks ambition. You buy the rights, then create an a slick cinematic ad for a new game, and when release day comes around, you pull a Ja Rule and leave everyone hanging and run off to the islands. 

I would pretend MEA never happened and return to the Milky Way by either making Destroy canon or setting future games at any point prior to the reaper invasion.

I personally would still love to see a game that deals with the aftermath of the reaper war, set maybe a year or two later. With entire systems cut off and what's left of the galactic population starving. New conflicts rising over not just resources but also political power. I'd love a game that lets the player decide whether they want to keep the council races in charge or help the underdogs get a piece of the cake at last. Either by proving everybody wrong about them or helping them get payback.

More reasonable would be a series of small scale unrelated games. Been talking with friends about how awesome it would be to play a Salarian private detective on Omega, discovering various (funny?) schemes. Maybe s/he has a vorcha bodyguard.

Or a real space pirate story...

The Mass Effect universe (Milky Way) is merely a setting. You can tell any story. Doesn't always have to be reaper scale apocalyptic. When MEA was first announced I thought we would get something like that perhaps. Instead we got more of the exact same. Bad guys threatening all life with horrible genetic experiments, accidentally discovering yet another mysterious extinct race... *yawn*

I just want to see more of the Milky Way races. Their cities, their customs. How they mix and mingle. This was what made the trilogy great. Fuck driving through empty desert planets. This already sucked in ME1.

Mass Effect is about a future galactic society.

I want to visit all the home worlds and just be a part of life in the Milky Way.

So... If I was filthy rich I'd make a non open world 40h Mass Effect game every 2-3 years featuring a protagonist of a different race in each.

Reminder: personal attacks are no go. A few posts cleaned up.

Ehh I'm not sure what the unity engine really is. For an engine, I'd just be thinking more of something that 1.could be more mod friendly 2.wont be a technical mess for a developer who can't learn it and 3. Something easy to use for anyone.  FB3 looks prettty but it's been an issue for Bioware since the start and I know people have a hard time using it for mods. Plus you have the perception that it's not meant for RPGs (which personally I think any engine can work for anything, it just needs the right tools and a mind behind it to work it.

I'd put up licenses for bids, so I could get even richer.

I'd find the best writers out there and pay them a ton of money to write a solid story.

I'd probably have it continue in Andromeda, since I have no desire to return to the Milky Way, and don't have any better ideas. I'd want it to lean further away from shooter and closer to an RPG. I'd expand the melee combat, and have a wider variety of weapons besides guns. I'd have "open world" level design, but make them smaller, with denser content, similar to how Deus EX: HR does it. Also like Deus Ex, I'd fill levels with multiple hidden paths and rooms, and grant EXP for discovering them. I'd also grant bonus EXP for things like pulling off combos and so on, cause I like systems that reward experimenting with all the different options.

Also, leveling would be quicker, and you would be able to max out all your abilities in one play-through, because why the hell not? All romance options would be accessible to male or female protags, and there would be a decent variety across genders and/or species. I'd have fewer side quests, but longer, and richer.

Oh, and couch co-op.

Unity seems to be the engine of choice for developers making isometric RPGs reminiscent of the old Infinity Engine games like Baldur's Gate and Planescape:  Torment.  Games like Pillars of Eternity, Shadowrun Returns, and Tyranny.

I don't know how moddable it is, but yeah, an easilly moddable game definitely boosts my interest level.

Well if I'm "I have ALL the money" rich, I'd be using it to RnD ways to get to the alternate universes where you guys are rich and in charge of ME and stopping you Particularly those whose canonize an ending.

Nah, but for serious now.

-hire Drew Karpyshyn and JMS for writing
-figure out a way to introduce time travel and/or alternate timelines for an in-universe re-do.
-Re-do the trilogy. The idea is to fix some of the issues, not massively rewrite the course of the series. It's not perfect, details would still need to be worked out obviously, but as an overview:

ME1: Starts with a normal-looking Saren (complete with both arms) going to the Citadel tower with a squad of asari commandos, taking it over to keep the Citadel open. C-Sec launches a full assault and drives him off. He loses the arm and is presumed dead. This is for all you "why didn't Saren just go to the tower in teh first place" bunch. Cue Eden Prime and the normal sequence of events. Also Liara and Shiala get merged into one character, Benezia's daughter, a commando who wanted to impress mother but got sacrificed. Makes their relationship more relevant to the plot, and gives the former more to work with in terms of falling from grace. Also makes the latter Shadow Broker stuff actually make some damn sense. We lose the naive archaeologist LI but she can always be worked back in as an NPC. Also, all LIs are playersexual. Rest of the game is more or less the same.

ME2: is now the story of Shepard looking to find allies/weapons in the Terminus since the Council and Alliance are feet-dragging dicks. They forbid or don't support him going in the Terminus but he flips them off and goes anyway. His allies however can't/won't do the same. The VS gives some bullshit about following orders, Liara/Shiala needs to go off and deal with her unstable biotics (thus setting her up for Ilium), Wrex is the same, Garrus is off training for C-Sec/Spectres, Tali's back with the Migrant Fleet. Before she goes, Liara/Shiala mentions something about Thorian memories indicating an ancient weapon which may work against the Reapers. There's also a fuzzy connection to the Collectors- they may know something about it since they're weird and collect things, or something. It's fuzzy. The Normandy goes looking for the Collectors and finds a ship, which immediately opens fire. The Normandy manages a short FTL jump, but something breaks and they arrive in an unknown system. The ship is rapidly deteriorating so Shepard orders everyone to the pods and makes a crash landing on the nearby planet (in the ship- there's no spacing, no brain death, no resurrection). He's still in shit condition and near-death but not for long- a Cerberus ship arrives and rescues them. Led by Miranda, they were also tailing the Collectors but broke off when the Normandy got hit. They're taken back to base where the surviving crew are returned to Alliance space none the wiser for who their benefactors are or what happened to Shepard or Joker. Shepard is still upgraded with cybernetics and shit to heal faster. Then Miranda takes him to TIM and the rest of ME2 can more or less progress the same from here. The Collectors are still targeting human colonies, but the mission is explicitly a squad infiltration mission to extract data on the weapon, or the Reapers with a secondary objective to disrupt Collector activity as opposed to an assault (12 people vs an assumed planet lol?). There is also talk of building connections to factions both in the Terminus and among the Council races to prepare for the upcoming war- things like Mordin and the STG, Samara and teh Justicars, Wrex/Okeer and the Krogan, Tali and the quarians, Aria, overtures being made to the Shadow Broker etc. The ending of the game is still fight the TermiReaper, blow/keep the base, but you also find plans for the Crucible- turns out the Collectors have also been going around trying to bury the plans, having been alerted that they still exist. TIM encourages you to keep the plans to yourself/upload only to Cerberus, citing Council incompetence and feet dragging, not to mention potential indoctrinated agents being made aware you now have the weapon. You decide what to do.
ME2 DLC: Mostly unchanged. Biggest difference is of course Shadow Broker. You notice the Broker helped the Collectors track down Crucible plans.  Liara/Shiala's been tracking him so it's time to go after him. There's no Feron or emotional yo-yoing but otherwise, it plays mostly the same. Oh, also, new rebuttal choices against that cunt Vasir, including a Renegade interrupt QTE where you empty your clip in her useless piece of shit corpse. It's like the ending to GoW3 where if you keep pushing the button, you can keep firing indefinitely. A squadmate will comment if you go too long, but that's about it.
New ME2 Expansion/DLC (after Arrival)- Hand of Shepard: The Council is still dragging its feet and the Alliance wants you in chains for that Batarian BS. Fuck that, you've wasted enough time. You have an impregnable base (the area beyond the Omega 4 relay), the makings of some awesome alliances, and a job to do. It's time to build the resistance (and the Crucible). Parts of this will be interjected within the main ME2 game but basically you build a new hub beyond Omega 4, the Shadow Broker moves in and you start gathering allies and resources. Through new missions, dialog and microtransactions (haha, just kidding, fuck EA) you start getting war assets and securing alliances including:
-Aria and the Omega system/Terminus fleets. This will cannibalize the ME3 missions. Cerberus will attack and you'll need to help Aria secure dominion over her turf (and your backdoor, really).
-Wrex and the krogan, Mordin and STG (setting up the genophage cure arc in ME3)
-Legion and the True Geth, Tali and teh Migrant Fleet (leading to a reworked Rannoch arc in ME3)
-Samara and the Justicars
-Rachni (if queen was spared)
-Ex Cerberus forces
-Hackett, Anderson and some insiders to the Alliance/Earthgov. They're covering with the Batarians for the moment.

You end with your own faction in the terminus, ready to pressure the feet-draggers into finally committing to prepare. As you're about to begin negotiations (or takeovers), the batarians declare war on humanity.

ME3: The batarians have declared war on humanity, humans and batarians are pointlessly fighting, the Council are pussying out on the sidelines as usual. You have to go deal with it. As you move in with your forces to try and get them to stand down, the Reapers attack mostly wiping out all sides. You're forced to leave batarian space to its fate while you scramble to Earth to get defense ready. You meet with Earth's leaders and they're almost as ineffectual as in the current game- not quite as bad, but almost. You bolster Alliance space with more geth, krogan, rachni (if spared) and misc Termius forces, but still it's not enough. The first battle for Earth is brutal and bloody and it's heartwrenching to abandon it, but you and Hackett make the call, leaving Anderson behind as in the current game. You go to the Council to demand assistance but they're in the same boat- pretty much back on track now. The main beats of the game more or less remain:
-the main arc: everything you're doing is still leading towards building the Crucible and deploying it.
-the krogan arc is virtually unchanged, apart from some setup you did in the previous DLC
-the coup: Udina is just indoctrinated for some reason. This is where you lose the Citadel. Unlike Saren, Udina is actually successful at keeping the arms open long enough for a Reaper to dock. The fleets go from fighting a desperate battle for defense to trying to evacuate as many people as you can, which isn't much. You get the Council out and maybe a few key players, but that's it. The relay network is shut down, well actually put into Reaper-only mode (because really, they'll still need to get around). Except you've planned for this, all your ships have the IFF installed and you're able to securely distribute it to allies as needed, via couriers, managed by EDI. The main hub now is Omega/your Redoubt base. This obviously affects the Citadel DLC.
-the Rannoch arc: while the geth willingly sided with you entirely, the Migrant Fleet was more or less strong-armed into it. With you distracted, they betray that and attack the geth back home with an experimental anti-synthetic weapon based on Reaper tech. This draws the Reapers and the diminishment of the local geth allows them to take over. Now you have to deal with this shit, much like in the current game, except you're a lot more pissed at the Quarians. The dynamic of who to trust/pick is also slightly different: while you trust the geth more and they can wage total war, their weakness of scattered consensus can be exploited by the Reapers again. The Reaper code may help, but Reapertech is usually bad. On the other side, the quarians... are just woobies. Don't you feel bad? There's more work to do with the details here, but I don't have the time now.
-the Cerberus arc: no, Cerberus won't be the ME Galactic Empire this time around. But they are indoctrinated and a mole inside your organization will betray you. And no, it's not Miranda. It's Brooks and the clone. They wreck/take over your redoubt and Omega- this allows the Omega DLC to still happen and will explain some of their martial forces (they stole them from you). It also cannibalizes the Citadel DLC, obviously. Sanctuary still goes down, Cronos still goes down, Miranda is there to flip off TIM.
-Endgame: this is the big one. First off, no moving Citadel Bullshit. When you attack, you attack Widow in a nice bookend/reversal of ME1. Full cinematic space battle with everything you've acquired thus far. Perhaps a multi-stage attack on other worlds as well, to distract the Reapers. The final mission is a Suicide Mission type thing on a larger scale- instead of deploying single squadmates for a task, you're deploying whole resources, like fleets, squads etc.
-Ending: no holokid, guiding hologram/AI comes from the Crucible, is an emergent intelligence (or Prothean VI although that's been done already) from all the modifications it went through, and it interfaces with the Citadel systems to figure out how to implement the options. Implementation requires Shepard's consciousness uploaded into the system (no more shoot the pipe, grab the rods bullshit) which leads to the final fight against Harbinger in Reaper cyberspace. Not sure how that would actually go, but some type of fun gameplay. After that it's choice time.
    -Destroy: SpaceEMP targeted to Reaper systems- accuracy based on EMS. High enough, only Reapers get wiped out, too low, everybody dies,     variations in the middle. Shepard clearly lives or dies based on EMS
    -Control: Distribute Shepard's consciousness into every Reaper and override/network them together. Single EMS threshold: above, success, below,     some Reapers are unaffected/resist and flee.
    -Synthesis: Attempt to resuscitate/free the Reapified aboard the Citadel and elsewhere. Some technobabble about Reaper tech control programming     forcing everything to perpetuate teh cycle but fully merging the organic and synthetic components in Reapers and Reaper creatures will free them from     this programming and could lead to unpredecented wonders. "Direct personality dissemination required"- Shepard does not survive in any way. High     EMS only.
-Reaper purpose/Leviathan origins: explored through exposition from the Crucible Intelligence and Leviathan. In the beginning there were Leviathans. They ruled the galaxy, enthralled people and pretty much considered themselves the apex of civilization. While their thrall civilizations stagnated and crumbled, their reign was eternal. Over time though, the Leviathans themselves finally started to succumb to this cultural entropy as well. Pure arrogance wouldn't allow the idea that they were as flawed as lesser beings (and the idea that Leviathan society might disappear altogether was unthinkable) so they searched for ways combat this and truly make their mark last forever. Realizing that organic whims were to blame, but synthetic programming was too rigid they came up with a hybrid solution, what they thought was the strength of both, the weaknesses of neither: Harbinger, the first Reaper. They decided not only that their entire race would go into Harbinger, but that all life would follow them into their new perfection. Some Leviathans resisted. A great war broke out. During the course of the war a weapon was created, a key to the Harbinger program that might be used to shut it down. They never had the chance to use it. Harbinger's side won. They liquified (almost) all Leviathans and assimilated them and moved on to the lesser races, harvesting only those ready or "worthy" of joining the new perfection. The survivors fled and hid but not before planting the seed of the weapon, so that one day someone might succeed where they failed. That key was the Crucible. For millions of years the Leviathans' arrogance and hubris persisted. The only question is, is this finally the cycle to end all cycles?

Aftermath: Up to you. There would be no post ME3 Milky Way content. Ever. At least not in game form. Maybe some speculative stuff, way down the line.

Otherwise, other products would include a revamp of Andromeda, with a focus on the Ark (explicitly made to escape the Reapers), its design and the journey there, a continuation of the Andromeda continuity, mid/interquels, smaller character-based stories in the Milky Way before the Reaper war, (maybe branching into other game genres as well) other media (books, maybe movies), toys, lunchboxes... hell I'll still milk it, why not.

I would have gotten a studio to realize my idea for a new Mass Effect game of course.

Ah. Fair enough.