I love this sort of thing, it's so fun! I've thought of six at the moment.
-Female Turian Sentinel: Her powers focus on defence and tanking. She considers herself a model soldier, tries to keep a completely professional attitude on ground missions and remains objective. On board the ship, she is much more relaxed and and has a thing for gallows humour. She's very competitive and keeps a running count of her kills compared to her squadmates. Initially, she'll be reluctant to tell you her personal opinion on your decisions (rather than making objective points). As your relationship develops though, she will become very honest about her thoughts and whether she agrees or disagrees with you.
-Asari Vanguard: A commando, hot-tempered and grumpy. Her powers tend to be offence-oriented. Prefers intimidation over diplomacy. She has a tendency to rub her comrades the wrong way, since she always speaks her mind. Despite her gruff demeanor, she has a good sense of humour and enjoys playing practical jokes on people. Ruthless to enemies, but dislikes pointless cruelty.
-Male Quarian Infiltrator: An exile, his skillset focuses on stealth and sabotage. Generally friendly and easy-going, if you don't mention the Migrant Fleet. He likes to spend a lot of time with the ship's pilot, nerding out over ships. He is homesick for ship life, but dislikes talking about the Fleet. He believes he was unjustly exiled, and harbours a grudge against them because of it.
-Female Human Engineer: Optimistic and idealistic, a savant with technology. Skillset includes things like drones, turrets, etc. Likes to create gadgets and play around with equipment to see what she can make. Sometimes leads to irritation from other crew mates if they were still using that equipment. She's fascinated by VI and AI. She feels a bit intimidated by the male human, and disapproves of his morals.
-Male Human Adept: Ruthless and practical. Has a high opinion of his biotic abilities and considers using them in combat to be a form of artistry. Tends to be an ends-justify-the-means type of guy. Mostly he likes to play it cool, but has a soft spot for fellow biotics, particularly those suffering from persecution (e.g. the L2s seeking reparations in ME1). Doesn't have a high opinion of the female human's personality, but has a lot of respect for her skill.
-Male Batarian Soldier: A decorated war hero, led the local defence against the Reapers on a batarian colony world. He managed to escape with a handful of survivors. He likes to play up the human-batarian rivalry, but doesn't mean anything by it. Cautious rather than idealistic and trusting, but keen to do the hero bit. He really doesn't like losing people or sacrifcing lives.
All but the batarian would be an LI. The third male LI could be the ship's pilot, making him relevant to the story and giving him input on ground missions (much like Joker). This would be perfect for me. Any extra people are just a bonus.
- Vorcha anomaly/experiment: Either a freak natural occurance or secret experiments (possibly by STG) results in an intelligent, eloquent vorcha. Obviously issues of his predicament and the shortcomings of his race are aplenty.
I really like this! It's probably the only way I'd want a vorcha in the team. They seem to simplistic otherwise.