You can switch your profile at anytime even mid fight....which is one thing I really don't like about the game, as there are no real classes and you can mix and match depending on how you feel. I actually have a maxed character with every skill maxed and I can use that character to do anything I want, from soldier to biotic to tech all at a press of a button, and the only disadvantage being armor and weapons not tailored to the new class.
You set a hotkey to one of four slots and you can then add three skills and a class per hotkey....you can also manually go in and change skills and class just like your father did during the initial attack run after he blows shield wall just before he interfaces with the environmental system. Medbay only lets you change how your skill points are allotted, and this allotment can then open different classes depending on how you spend your skill points, but after gaining enough levels most/all classes will be available.