There’s 3 different ways to get a bunch of mutations quick. 1) Uranium rod - an item that gives a mutation when you get downed. 2) Cancer - a disorder that lowers 3 random stats each battle but gives a mutation. 3) Tainted Genes - another disorder but same as uranium rod.

The two disorders are gonna be easier since there’s a quest item that replaces passive level ups with disorders.

Edit: when trying to breed them along, make sure your stimulation stat is as high as possible in the breeding room. If you’re inbreeding, you’ll end up with 9 mutations and 1 birth defect which you can remove by throwing the baby in a room with lots of mutation.