It all depends on the site, to be honest. Some pet sites focus on collectibles and breeding, while others don’t emphasize those aspects. I don’t think there should be a limit actually, especially if the pet site has plenty of server space.
If you wanted to propose a limit, I’d say starting off with 10-20 pets is a good way to start the game with a chance of expansion.
For sites centered around breeding, there’s usually a limit of 60–90 pets per user, with options to expand space through account upgrades or cash purchases.
For example:
Marapets actually allows 120 pets per user. This limit was 100 pets for years but was recently increased.
Subeta users start off with a limit of 10 pets per user, but additional slots can be purchased through the Millionaire Lodge.
Neopets limits accounts to 20 pets, but premium subscribers can have up to 24 pets.
Xanje doesn’t have a pet limit, allowing users to collect and breed as many pets as they like. The site is similar to Pokémon, encouraging players to “catch them all.”
Aywas is another game without a limit, as users can expand their pet slots by purchasing items with points.
Each site has its unique approach, tailored to different types of players and gameplay styles.