Can Players Control What 50 Pets are Summoned at Camp?

Really hoping we can control that, I just got done getting 99 pets. But I only want certain ones to appear at camp.

If anyone needs help getting tough pets, like Ruddy Shelduck, Whisling Duck, Smew, all the colored Forest Rabbits, Desert Rabbit, Snowfield creatures, and etc. Just ask, I was able to get all of them.

I'm guessing they did a few adjustments that weren't in the 1.11 patch notes, because the spawns are much more generous now.