with befriend as a skill, it's very possible this is already planned -- but I think it would be neat to have a chance of coming across new not-cats while adventuring that will return home with you! Search to find a not-cat hiding from nearby monsters, Force rubble away from a trapped cat, Sneak around a monster to create a distraction... or use skills to impress them! maybe skill challenges where the new not-cat wants to see if you're up to their standards with a display of a particular skill, physical or knowledge based. not sure you'll be good enough at what they want? attempt to Bluff, Intimidate, or Befriend instead.
possibly the new not-cat could have stats based around what skill they want a display of, either something that matches (Clever cat wants to see knowledge skills) or something that makes up for what they lack (low Strength cat wants to see Strength skills, etc).
kittens could maybe be found through adventuring? but the implications of that are pretty sad
this was longer than intended, oops! I really enjoy the idea of more ways to encounter new not-cats to bring to the village, and even if it's a very rare encounter, I think it would add a fun bit of flavour.