Breed the Next Generation
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The cats that survive Mewgenics come home changed, and the store is explicit about what they carry back: scars, experience and sometimes extra heads.
What comes home
Cats that return home carry scars, experience and sometimes more heads, which then becomes the raw material for the next generation. That is the point where a tactics game turns into a breeding game: the run is not finished when you get home, it is where the following run gets decided.
Pass it down
You pass down strange skills and mutations, tinker with your bloodline and tackle genetic quirks to build ever stranger, more powerful cats. Because the inheritance is described as strange rather than optimal, the interesting decision is usually what you are willing to carry forward rather than what is strictly strongest.
The kitten question
The store describes agonizing strategic choices about whether to keep a cute kitten or give it to one of the many NPCs to upgrade your house. That is the whole tension in a single line: a cat can be a fighter or a resource, and the game expects you to decide which.
The fights those cats are bred for are covered in running the cat loop. The scale of the ability pool is covered in planning around hundreds of abilities.
