The answer, apparently, is seven, with the help of Legion, Joker, EDI, Kasumi and three Tali'Zorahs. I'm suddenly jealous that I could never bring more than two companions with my Shepard in a party.
BioWare had a photobooth set up at PAX, capturing many of the best Mass Effect and Dragon Age cosplayers the convention had to offer. (Along with one slightly inexplicable red power ranger.) The photography is from N8Zim Photography, the same folks who brought us that great Shepard and Phantom couple from DragonCon.
BioWare's got a whole great huge gallery from the photobooth over on Pinterest. See the saga of Kai Leng and his dastardly cereal theft below, or head on over to the link for some really great costumes. (Like Fenris. And Varric. And Anora. And FemShep shooting Kai Leng in the face. And...)
PAX Photo Booth by N8Zim Photography [BioWare Official Pinterest Page]