you can sure, but it's an even bigger pain in the ass because you have to switch character voices all the time, and it's also much more difficult for the reader. At least with third-person, you have a more-or-less consistent narrative voice. If you're doing multiple first-person narration, you have to change the entire narrative style every time you switch. (Or you can not change the narrative style, and you get garbage like Robert A. Heinlein's Number of the Beast, where you have four first-person narratives THAT ALL SOUND EXACTLY THE SAME.)
I am not saying it is not challenge but it can make an interesting book and it's not like it hasn't been done before. If you have different first person narratives you can tell the same story from different perspectives.
Would your different characters see the same events in the same way?