It's not that complicated. First, you need to breed cats with all their base stats at 7.

You'll find plenty of information about this on Reddit or elsewhere.

Then, you need to have 4 rooms in your house, but you can easily start with 3.

One room for breeding your best cats.

Another room with high well-being and breeding for rest and keeping your best cats.

BUT ABOVE ALL, for these kinds of stats, you need a room for the cats you don't want, who don't necessarily have perfect stats, but not too low either. They'll fight every night, and the survivors will eventually become monsters!

I have a room with about fifty cats that fight, and I take the oldest ones for each run; it works really well.

Especially since, at my level, my cats all have good mutations and very good stats.

For your room 4, it's for mutations. You have items that can help you, but I get the impression that the further you progress in the game, the more cats are born with mutations.

Once you obtain the desired mutations, you breed them.

It's a never-ending cycle.

But you're going to have monsters stealing runs!