What is the right number of solos to audition for in your ensemble?
I think the right answer is: as many as you’re prepared to sing.
You shouldn’t try solos in rehearsal (let alone in performance) if you’re not prepared, but barring that, there should be no max. You might be concerned about looking like a solo hog or wasting rehearsal time, but the fact is that your preparation is good for your ensemble mates to hear, and your enthusiasm should be infectious with the rest of the group.
Try the solos. It’s good for you, it’s good for your fellow singers, and it’s good for the ensemble as a whole.