In a fanfiction, the rooster could be the key to a mystery. There could be an old legend among the pets that a rooster holds the power to unlock a hidden treasure. The rooster doesn't even know about this power at first. Max and his friends team up with the rooster to figure out what this power is and where the treasure might be. Along the way, they face many challenges, like avoiding the dog catcher and outsmarting a group of mischievous squirrels.
A rooster in a fanfiction could be a messenger for the pets. Since roosters are known for their early morning calls, he could be the one to wake up all the pets for their secret meetings or adventures.
Perhaps the rooster in the Secret Life of Pets fanfiction is an escaped circus animal. He has all these amazing tricks that he shows off to the other pets. The pets are both amazed and a little scared at first, but as they get to know him, they learn that he's just a friendly fellow looking for a new home. He could even teach some of the other pets his circus tricks, like how to balance on a tightrope or jump through hoops.