I play one character at a time. I do, however, keep many saves for every playthrough so that I can return later to revisit my decisions and class- and race-dependent elements.
I have one "personal canon" Inquisitor. Maelyn Trevelyan, non-Andrastian human mage (Knight Enchanter), allied with mages, Celene rules alone, Wardens allied, Inquisition rules through the Secrecy branch, Iron Bull leaves the Qun, Cole becomes more human (liable to change), Cassandra becomes Divine, Cullen stops taking lyrium, Blackwall sent to the Wardens (liable to change). I will be refining her story through additional playthrough, and I'm absolutely torn about the Well of Sorrows, because it's about, well, I think it would not be inaccurate to say it's about the two things she values most: knowledge and her individual autonomy. To see them in conflict is really, really, *really* hard. So far I've not used the Well, but I don't know if I'll let that decision stand.