When you adopt yes, each pet species has a set amount, but it's differs each month, you can adopt the full amount, which is a good idea so you have possible doubles or spares to swap and trade. When you see 'Adopt 1' click the little down pointing arrow next to it, and the box will drop down to reveal how many of a pet litter can be adopted.
Then you can trade for more pets.
I have over 3000 pets in one of my groups, and hundreds in others.
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