This app was mentioned in 3 comments, with an average of 1.33 upvotes
Happy Pet Story is an option I saw a lot people who liked PS played, Pet Paradise was made by fans of Pet Society.
A while ago a twitter page (@PetsPals1) for a future game followed me, though they haven't posted in a while I thought maybe you'd be interested in following them since they are apparently making a Pet Society clone of sorts.
Edit: You can also preregister for Kawaii Home Design. They already have another game called Sky Islands where you can decorate/manage your resort.
I think they're referring to a phone game, Happy Pet Story.