You have to get the follow the leader beginner skill. I think you start it at pet park in henesys BUT I don't remember for sure since I did it a while ago. I think it involves buying a nx pet snack or something.
Wel, you start it in hene at the pet guy, continue with his following quests and then you gotta go to cs and buy some fruit snack that allots you have to multiple pets out (idk whats it called but it should b under pet, then item) then u give the guy the treat and boom you have the follow the leader beginner skill and u have up to three pets out at once and one will be the leader.
Sources: I've done and have the skill