Well, here we go.
Liara: First off, I'd keep her on the Normandy, and have the war assets room be replaced with the Shadow Broker hub, seeing as the Hagalaz base is kaput. Not just those monitors, but banks of hard drives and coolant and, well, tech. Early on, I'd have an event where she is almost killed, and Shepard CAN, doesn't have to, but can convince her that the role of the Shadow Broker is far too important to have her running around in battle. If Shepard does talk her into staying safe, she provides you with a biotic squadmate. Guess who? Well, turns out Tela Vasir didn't actually die on Illium, just passed out due to shock (or whatever the Asari equivalent is.) We do just leave her there if I remember correctly. She would be the first vanguard squadmate and we'd get an actual Spectre to work with, looking at you VS. Liara would still get a lot of interaction in this scenario, but won't be risking the whole "most powerful information broker in the galaxy."
Garrus: More or less the same, but a lot more content. This can include rescuing his sister from Palaven, chasing down an indoctrinated Spectre on the Citadel, and have a more interactive role in defeating the bottle rebellion/sniping contest. Add in more dialogue, and other stuff.
Miranda: First off, Shepard only repainted the Normandy, maybe back to the red and black scheme of the original. She did not go into Alliance custody, seeing as she is no longer an Alliance citizen, is not under their jurisdiction, and can very well be reinstated as a goddamn Spectre again. Any loyalty to Cerberus is cut. Miranda is, of course, Shepard's XO. As Liara is regardless moved to the war assets area, Miranda has kept her old office. She leads the crew to Cerberus' outposts and is insistent in investigating both them and her father. She knows a lot; she is possibly the best possible asset. During fighting the Reapers, the Normandy consistently attacks, not defends against, Cerberus with her intel. Cerberus takes a reduced roll in the game, however. They're on the run, like in the original. Miranda, of course, gets more content, and early on her sister is rescued so her head is clear.
Thane: I'd keep it mostly the same, but change what causes his death, and have him give his advice and wisdom as well to Shepard in the hospital. Instead of running at Kai Leng like a fool, he takes on Leng and his 4-5 phantom minions at the same time, killing the phantoms and wounding Leng badly before he is stabbed, while Shepard and Co protect the councilorS during a large scale assassination attempt, not a coup. Death scene in the hospital remains the same, so goddamn touching.
Samara: Joins up if she survives the Monastery events, taking her place in the observation lounge. She and Shepard get a lot of more philosophical and deep dialogue on the ship, up to the point where before the final assault, where the combined might of the galaxy is moving to take on the Reapers head on at Earth, no crucible, and break their back, as its established that the majority, maybe like 60%, is stationed at Earth to protect the birth of the baby Reaper, Shepard visits her in her cabin instead of the other way around, where there's more touching stuff and, well, something happens, Citadel DLC like.
Jack: Well, this is tough. Well, I'm trying to make this so as many people as possible would be okay, but I never really liked Jack. I have no idea how to do her justice. I don't think she should be on the Normandy, we can't have too many biotics, already have 3 so far, but I'd just give her a lot more cameos and meet-ups on the Citadel.
Kasumi: Meh. Same, with more meet-ups around, maybe encounter her as you raid Cerberus. I do really like her, but she doesn't fit into the ME narrative well.
Tali: I'd have an encounter with her leading a new squad of marines, with Kal'Reegar, defending a fuel depot where the Fleet plans to refuel in a couple of days before moving toward the Perseus Veil, early on in the game. I'd keep her the same throughout the Rannoch arc and beyond, but as with almost everyone, boost her content and give her a goddamn face, if romanced.
Legion: Same, but doesn't need to do that "artificial personality dissemination." If the Quarians die, he takes Tali's place, but otherwise, fights elsewhere in the war. Makes an apperance again leading a huge, and absolutely huge, force of Geth on Earth.
Jacob:
. Same, maybe less as before.
Zaeed: On the Citadel more, with more meet-ups. Is more or less training any capable and willing refugees into a formidably defense militia for the Citadel after helping with the Volus event.
James: Same. He doesn't mean much to the plot, but I like the guy.
Ashley/Kaidan: Stayed on Earth with Anderson to lead the resistance. You can talk, but they mainly stay back. Instead, we get Major Kirrahe, the most badass Salarian this side of Mordin. You find him, not bugging, but tapping into the SB feeds on the Normandy for the STG. Shepard convinces him to stop, or doesn't, and invites him to fight with her. Tough, Soldier type squadmate, but with a single unique tech attack. He will hold the line.
Grunt: Never left the Normandy. Shepard is his battlemaster, he will fight with her, for her, and by her. Hashed out, possible parent-son type relationship between the two. We need a Krogan. We didn't get a Krogan. It was an abomination. Heheheheheh.
EDI: Same, but less sexbot. More realistic android body that she uses at times because she wants to feel more organic and less ship-chassis. No squadmate.
Aria: The Reapers destroyed Omega, and she comes to you to give her an opportunity to punish them for breaking Omega's one rule. She and Samara will likely get in each other's faces at times. Brings with her, if Shepard agrees, Bray. Engineer, mainly for variation.
Javik: Same.
So, squadmates:
Biotic: Liara/Vasir, Miranda, Aria, Javik
Soldier: Garrus, Kirrahe, Jimmy Vega, Grunt
Techies: Bray, Tali/Legion, Kirrahe(he serves as both)
Mordin keeps up the same as well; more patter songs though.