As a 1e GM, I'd probably allow this, but I'd require you to take the Half-Dragon and Two-Headed templates and put you a few levels behind for it.
Since they're two-headed, with one chromatic and one metallic, I can imagine them learning to work together to focus and survive but still constantly bicker with each other outside danger because of differential alignments. Except instead of being some weird mental personalities against each other, the rest of the party has to listen to it and deal with it.