So, a question has arisen for my friends and me. We've all picked up MAG but are spread across all three factions. We thought it would be simple enough to just make another toon but that doesn't seem possible. You can only make one character as far as I can tell. So, my question is am I missing something, is this something that is unlocked later on, or are we going to have to pick a faction and everyone who has guys of another faction will have to start from scratch?

It seems like you can only have one character, which is kinda the developer's intention. Other factions will apparently try to recruit you, but the idea is to get a sense of alliance with your chosen faction.
 
I recommend if you really want to play with your friends to delete your characters, decide upon a faction you all agree on and start over, yo.

Not being able to make another character seems strange considering there appears to be room for three characters on the start screen and you can get trophies for reaching level 60 in all three factions. I'm still holding out hope that it unlocks at a higher level.

Not as far as I know.  You have to delete it.

" Not as far as I know.  You have to delete it. "