Actually the battle idea might not be suitable to the poor LPP's if they die. I was thinking that we might make them just hav a friendly match that won't make LPPs die but instead make them stronger on one of their stats. ( and lets the owner of the winning pet take something from the loser's inventory) There should be a shop too. As ladycfii said:
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you could get very creative with what the game player could do with the output of breeding efforts: dead fish fertilizer, selling seed packets, even a little chemistry lab on the side for developing new concoctions to pour on your plants or dump in your fish tank!

We could make something that we find in our pet's yard to make new toys or something to play with the LPP! Maybe you should also make a pond somewhere so the LPP can play with water toys and swim! Like what i saw somewhere else, U should also allow 2 LPPs playing together! (no fighting unless u are battling other players only)