No, you can't, or at least can't do so well. There just isn't enough material in the right places to make a good fishtail button out of a p-lip stem. Also, hand cutting a button in vulcanite requires pretty tremendous levels of skill and experience, as well as the right tools, so even if you did have enough material to fashion a button, it's just a really bad idea.
Sykes
Edit: I think it's possible that on very specific stem shapes the above may not be true and it might be--in very narrow circumstances--to have enough material on a p-lip stem that this is--in a literal sense--possible. But hand cutting a button from rod is hard; hand cutting a button from a differently shaped button with different internal configuration? Really close to impossible to do well.