What should BioWare do now with Mass Effect?

Scrap it and make KOTOR 3

Just kidding, they would probably just ruin that too.

Scrap it, and stop butchering it until they can re-learn the basics of listening to customers, and fixing bugs BEFORE release.

Same goes for Dragon Age.

It seems the majority are in favor of BioWare picking up where they left off. Truth be told, I'm curious to see what BioWare Edmonton would do with Andromeda. They obviously did not create it, so it would be fascinating to see what they keep and what they drop with a sequel. It just is more feasible and makes more sense to continue off of the foundation that has been laid. Why start all over again and potentially run into the same pitfalls that Andromeda had?

I'd rather, if we went back to the Milky Way. If they'd continue in Andromeda, then I'd have to force myself to suffer through the campaign and it hasn't happened yet. I've played ME1 27 times, ME2 31 times and ME3 22 times, but I just can't finish ME:A after ~20 hours.
They could come up with a story that runs parallel with the trilogy's timeline, some cool adventure on a smaller scale.

unless i'm mistaken, when there was discussion of where and when a new ME should be, Casey Hudson was in favor of setting ME4 in a far distant future, to be free of Shepard and the Reapers.
So working on something post MEA would make sense .
But who knows, the future iteration of the game feels more remote than our neighboring galaxy.

I'd go for broke and attempt to create a true Mass Effect 4 continuing the themes and ideas of the trilogy set in Andromeda 1000+ years later bringing back the Geth as the series main antagonists.

The premise would be a pseudo-sequel to the original trilogy in the distant future where unbeknownst to us the majority of the orthodox Geth had already fled the Reapers decades prior to ME1 having encountered Sovereign (and the truth about the Mass Relays and the extinction cycles) 50-100 years before we did so the majority of the Geth had not only long since escaped the firing of the crucible but have been building their future in Andromeda far (considerably) longer than we have.

By now a new council and spectres have been re-established, the new council space is as developed as the old one was (less spread out but more densely populated), population in the billions, each species has colonised their own regions which are connected by a new Mass Relay network. The Kett were defeated by the Krogan who along with the Angara are part of the new council.

The Geth are considered a historical, previously thought extinct species, although there are rumors that they have returned. Worryingly Quarian scout ships have been disappearing lately and these might be connected. Following leads it is discovered they found the remains of a Geth ship and several Quarian ships looking for missing Quarians traced it's origins and discovered Geth space and were supposedly attacked. The council species are terrified that the Geth are amassing on their borders and have requested the assistance of the spectres to resolve this matter peacefully if possible as the first line of defence before military engagement.

Mass Effect 4 would be an opportunity to right wrongs of ME3's ending and answer the question once and for all of what happens after Destroy when free-willed synthetics have returned and the Reapers are long gone... What happens then? Was Javik correct that man must conquer machines as part of our evolution? Or can we achieve what the Reapers and Protheans failed to do on our own terms without resorting to space magic contrivance or genocidal barbarism?

Where ME3 (Reapers) failed and where I think ME4 could succeed is in acknowledging the importance of the fact that the Geth were not in fact created by organics, their consciousness developed organically much like ours; so they are not subject to same flawed (creator-created) logical imperfections which plagued previous synthetics throughout history including the Reapers. Hence the Reapers assumptions were flawed and never applied to the Geth. The only obstacle to achieving peace is our organic nature (distrust) which can be overcome only through logic and understanding which we gain throughout our adventure. This echoes and explains Shepard's achievements on Rannoch many centuries earlier.

The new protagonist uncovers the truths and surrounding background details about Leviathan-Reapers, their cycles and various theories about synthetic and organic nature through their interaction with the Geth and Quarians as the plot advances and though plenty of conflict and attempts at diplomacy you eventually avert full scale organic-synthetic war. Although peace with other Synthetic species throughout Andromeda (who may or may not be subject to the same organic flaws which lead to the Reaper cycles) is by no means guaranteed this is a crucial first step in ensuring our collective survival outside of the reaper-cycles, overcoming the narrative problems of ME3-MEA and establishing a solid foundation for future games.

Because?

Sovereign approached the Geth decades before ME1 that's common knowledge so they had the same means motive and opportunity we had. We did exactly the same thing with the Andromeda initiative as soon as the cat was out of the bag prior to the invasion so it stands to reason they would attempt to do the same had they known decades before we did. Yes it's a self-conscious Episode VII/New Home-esque homage to ME1 and an attempt at a soft reboot of the series that attempts to acknowledge and build upon the ME3 ending while moving beyond it and sweeping MEA under the carpet.

Moving the series to Andromeda in the first place was a cop out. Trying to make Lemonade here with the lemons we were handed. Might as well mould it into the setting we all fell in love with if we otherwise will never see the milky way galaxy again short of a hard resetting the entire franchise and starting from scratch all over again.

It's forced and contrived... more focused on a personal desire to see the Reapers back than it is on connecting things with a good story. 

Firstly, the heretic geth allied with the Reapers but the true geth had no motivation to flee them.  They stayed behind the Perseus Veil and tended Rannoch as a memorial to their Creators (per Legion in ME2).  There is no indicated by Legion of true geth disappearing out of the network (and he would have known because their all connected).  People went on and on about how Shepard & co. should have known about the Initiative... Well, it's the same issue intensified with having geth fleeing the galaxy.

I would really rather to just let the OT end where it did in ME3 and I wish the malcontents would just let Bioware continue with a NEW STORY in Andromeda.  I found the hints they put out at the end of ME:A have a lot of potential.  They obviously have a planned story in mind.  For Christ's sake, let them write it!