New squadmates you would want

A salarian (an infiltrator esque type squaddie with a shotgun; think like a geth hunter from ME3) and/or asari commando.
A batarian; this was some huge missed potential in the OT imho, would love to see one now. But could enough of them been packed onto the Quarian ark?
A Quarian. Would love another female, but I guess in fairness, it's time for a male.

I was thinking more or a Pathfinder Squad-mate Exchange program. Let the squad-mates experience how it would be to work under a different Pathfinder:
Cora exchanged to the Salarian team(yeah she'd want to go to the Asari)
Liam exchanged to the Turian team(let him learn some disapline)
Vetra exchanged to the Asari team(reasons)
PeeBee exchanged to the Quarian team(if the Quarian Arks shows up, just to see her in a full containment suit)

We can still meet-up, with our old team-mates at Meridian, or the Nexus, to talk or continue/cancel our LI.

We already had one, her name is Cora.

Asariboo Commando =/= Asari Commando 

I know I want a super sexy female angara, Avela would morel likely be that candidate as an archivist about the tempest.

Avela :

I want a squadmate that will surprise us - something completely unexpected, whether in species or build/class or story. I don't care what the specifics are, I just want to feel like they've done something new with them.

Romancable vorcha for females and males, LOL.

A proper soldier/commando asari. No more Liara or her proxy Peebee styles ones. Hopefully another squad mate who can use an assault rifle.

- Male Batarian. Some real badass, criminal, thief, murderer, assassin. Someone really bad. Pure fun for Renegade
- Volus. Some funny tech guy. He has to be full of sh...
- NEW RACE. Just someone new. But not so friendly as Jaal or anyone else. Let me work hard for his trust, no 1-2 missions pattern and done.
- Vorcha scientist. I know how it sounds, but everyone deserve a chance.

1. Ixy Zorbant A demure (or emo) Salarian woman who rejects the elitist intellectualism of most Salarians. She speaks slowly, is uninterested in science or technology and is forthcoming where most Salarians are reserved or prudish. She is on a journey of enlightenment and self actualization. Possibly looking for ways to extend her live well past the 40 something years a Salarian should get (which is all the strange given her young age). She is not an experienced combatant but was formerly a trooper with some exiles and displays a natural talent for battle. 

2. Jeff An aspiring young Krogan artist and musician exiled by his father and told not to come back home without 5 war stories. He's a sensitive soul with powerful biotics. Powerful enough to somehow end up on the crew.

3. Xara Th'ralus (Xeetee) Asari Sherlock Holmes, the greatest detective in Andromeda (formerly the Milky Way). She can't be separated from her long coat, her brow is often furrowed in faux concentration, she is condescending, self aggrandizing, blunt and her wit is both dry and derisive. She is hunted by an enigmatic nemesis who followed her from the milky way. She is - by her own description - a sociopath who hardly displays emotions besides neurotic disappointment (when struggling to crack a case) or slight amusement (when things are going her way). Still, she is capable of love. It just won't really feel like it

4. Walter Colwell An old human man: veteran of the First Contact War and former President of the United North American States who was so unpopular he came all the way to Andromeda for a fresh start. A natural politician: charismatic, persuasive and possessing a mind like a steel trap even in his old age. His motives are unclear but he seems driven by a need for domination and you wonder if you can ever trust him 100%. He fights with the aid of a bulky cyborg-body-suit type thing that moves his old bones around as if he's still an officer on the frontlines of Shanxi.  Outside of the suit he is a healthy but physically limited man of 70

5. Dhonne A Batarian man who deeply believes in the Batarian Hegemony and who's primary delusion is that he can bring the Hegemony to Andromeda. A highly, highly skilled combatant who probably served as one of the Hegemony's top assassin's or body guards but refuses to acknowledge where his skills come from. In the Milky Way, he'd be your enemy. In Andromeda, his fighting skills and influence over the Batarian arrivals make him a valuable member of any team. You just hope you can help him see the light some day

6. Tali

7. Calo Terion The nastiest, most sinister, rigid and cruel Turian we have ever seen in a Mass Effect game. A career military official who joins the crew out of absolute necessity with all the good intentions in the world but a heart of frigid, immobile steel and a sadistic taste for bloodshed and the torture of captives. 

just some random ideas

edit: added names cuz I was having too much fun

Batarian pls.

Other than that, I'll take a Kett or a Geth.