The pharmacy is pretty useless beyond filling up some collections and getting certain items for certain recipes
So maybe illnesses to spice things up?
Not sure if it would be possible with the battle system, but each illness could affect a stat (e.g. a cold could affect strength, overgrown nails reduce speed by, say, 10%, but increase strength by 5% because nails hurt, a fever could cause a pet to lose 20 hunger a day instead of 10, and so on)
Pets would be more likely to get diseases if they get hungry or bored (finally a use for playing with a creatu!)
To add to that, instead of fleas, a pet could be afflicted with a flea-like Creatu. When they have the condition, upon curing there could be a small chance (5%?) of getting one of the eggs for incubating and hatching
Of course, not every pet can get every disease. In fact, I'd bet none of them could get every disease. RSTUs would naturally be immune to all normal diseases. Maybe they could have one or two glitches instead
Summary:
-Pets can get diseases
-If possible, diseases can affect stats and even how fast a pet gets hungry or bored
-The hungrier and more bored a pet is, the easier it is for them to get ill
-Flea-like creatu can have their eggs rarely gathered if a pet has fleas and is cured
-Different diseases and disease catch rates for different pets, with some overlaps