You can only have 1 Kuku pet summoned at once though.
The Kuku pet is sometimes given out during events or through attendance rewards (eg. You can also obtain a free Desert Fox pet by completing Deve’s Encyclopedia and are rewarded with a free cat or dog pet when you have played the game for over 5,00 hours. The quests are listed under Pets, Loyal Companions.You can find the quests by pressing to open your quest log, then going to the Suggested tab.The pets are only available once per family. There are 5 pets you can obtain completely free by completing the main story quests.