Hello all, I don't think these have been suggested before? Didn't see them at least. What if, when speaking to a cat, there was a random chance for them to give you a side quest (sort of like how gifts randomly get rolled). This might have to be semi-seasonal (i.e. no herbs during winter, unless it was meant as an extra challenge or something?), and could be anything from food to herbs to insects or whatever. Different quests could have different rewards, and could act as an additional chance to boost reputation that day, perhaps? They could also possibly reward mews, or food, or herbs or such (i.e. A cat might say "hey, could you bring me some goldenseal? I'll give you 5 mews for it" or something. Prices could be higher than the default shop sell price.)
In addition, maybe you could spar with some of the cats as your reputation with them rises? This might have to be restricted to certain cats (i.e. in the forest colony, Scout and Sarge seem a lot more likely to want to spar than Missy and Lyrus, etc.), but could be a "safe" but inefficient way of earning exp (since you'd only be fighting one cat at a time, and not a lot at once like in battles, which tends to be a faster way of getting exp). You could maybe still earn the standard amount for defeating them, but there would be no chance of death (if your health got too low the cat could say something like "Hey, you look a little worn out-- maybe we should take a break", or, if you tried to start a battle with low health "I dunno-- you look too tired to spar!" or something). This could maybe raise reputation as well, but reputation reward might have to be locked to once or twice a day so it couldn't be exploited.