In the game, you fish, and sometimes you catch a fish that turns your pet into a monster for a few minutes. Otherwise the fish are pretty useless. What if that transformation left a lasting impact on the pet, a taint? What if turning your pet into a spider a few times boosts your pet's poison armor rating by 10 each time, for permanent and cumulative effect. What if it also gives a chance to poison on attack, say 1% per transformation, per spider egg? Same for vampire spider, only that also activates a permanent low-grade vampire/health steal point total which accumulates.
And if your pet turns into a crab, that boosts electric armor by 10, each transformation, permanently. And that your pet will have a chance to shock during fights, and also emit a chance for AOE shock radius when struck, some low chance that accumulates around 1% per crab egg fed to the pet.
Apply various fish and eggs as needed, in the background, and increment the animal's stats for this bonus to work properly.
In theory, this would be easier to setup than allowing enchanting of the collar and tags, or adding ring slots for the pet, though those are a fine idea too.