If you’re creating a show with a partner, first decide whether you’re actually doing the show together or whether you’re just tolerating each other.
I’ve seen plenty of two-handers where one person does their thing, the other does theirs, and maybe they finish with a duet. If your show is supposed to be about the two of you, make sure the majority of your stage time is spent together. Make the most of what you’ve got and don’t try and compete with each other for solo spots. You’re a team and two is (usually) better than one.