Actually I do have 3 suggestions too:
1. Asign gender to monsters.
This doesn't have to make any significant difference, except maybe when merging monsters, (with fusion), but it would help us in role play, by imagining, presenting the monsters we breed to ourselves.
2. As it was already suggested recently, a way, a method, at least a chance or possibility to extend our monster's life time, let's say from current maximum 5 to 10, or even 15 years.
I don't consider that for too many, nor for unrealistic, after all some animals can even live for much longer than that. (I have an over 18 years old cat in real life for example)
Normally this can be monster-type, monster-breed dependent, for example 4-legged mammal type monsters, or goblins, zombies, faeries, dragons could live for significantly longer than worm, insect, bird, plant, fish, or slime type ones
Hybrid monsters normally could also have an increased or decreased lifetime accordingly, depending on what types of breeds they are combined from.
3. Add dog, or even wolf-type monsters to the game!
Personally I admire cats and, generally, dislike dogs, but I bet many players would gladly select and play those...after all dogs are (at least) just as popular as cats.
Normally, those dog type monsters would initially hate cat types, and vice versa, which could be manifested in colosseum battles for example, with some characteristics, extras, or passive skills, like "inflicting 50% more damage to eachother".