I always had 4 sets: Low heat cycle R6s, A set of low heat cycle A6s for qualies and cold damp tracks that weren't really wet, a set of R6s that were high heat cycled for practice etc, and a set of Hoosier Dirt Stockers, teh all time king of IT rain tires.
BUT, if I was REALLY prepared, I'd have had a set of Inters. Ideally they would be A compounds with medium groves, but, nobody makes those, so the next best thing was a good street tire.
But MOST of the time, it's either getting wetter, or getting dryer, and you need to plan accordingly. Rare is the race where you just don't know. (Although I guessed wrong badly once, I've been right far more often and the results followed)
BUT, eliminate the whole R and A thing, and at BEST you have three sets: Full tread, (wets), some tread, (inters) and barely treads (drys).
You could 'get by" with two sets easy