Short Answer: Go to the dogs
WC Fields famously hated to share the screen with kids and animals, because the always command attention even a veteran vaudevillian could not compete with. Bill Waterson, creator of Calvin and Hobbes, noticed this too, and so refused let Hobbes the tiger appear without Calvin, although Calvin could appear without Hobbes; he did not want Hobbes, he said, to take over the way Snoopy had taken over from Charlie Brown.
That said, the MIB franchise is in trouble, both in general after the relatively poor performance of the "International" spinoff (also, PLEASE let me work in an industry in which $200 million-plus returns is a disappointment) and the... shenanigans of its star.
Still, the MIB movies have a secret weapon: Frank the Pug.
But, wait-- won't an animal take over the screen?
Let him. If we know that people watch animals being silly, let them see it on the big screen.
In the now-upcoming Guardians of the Galaxy movie, we learn that [SPOILERS] Cosmo the astronaut dog is psychic and we also learn Rocket the Raccoon's origin. From Baby Groot to Grogu (formerly "Baby Yoda") franchises are increasingly willing to tick off the WC Fieldses of today and let the cute run wild.
So let's see a whole movie about Frank the Pug, with the story centered around him and his kind, his origin, etc. Put him in danger and let him help Agent J save him.
The franchise has already done the international shtick, with a woman agent, and the time-travel schtick. Now it's time to visit Planet Pug.
They have a talking alien dog. Futurama's Nibbler went from being comic relief to one of the main drivers of the plot. Same with Olaf in Frozen. If you have a cute character that the public likes, let them like it more.