Some origins would allow more changes than other. For example, Astarion defininf trait is that he is a vampire. But he could be female, any character class, with any stats and, basically, any skill set and it would work the same. Laezel could change everything but her race.

Gale, could change race, stats, sex and even background. Everything but his class. Same with Wyll, who could be any race, sex, and have any stats as long as he remains a warlock. And same with Shadow heart, who only needs to remain a priest of shar.

But as someone pointed out, that might affect scenes and add extra work that it would be better used in custom characters.