A sequel will place Baby Co. and Puppy Co. in an Enemy Mine scenario.
Boss Baby tells Tim it'll be the end of Baby Co. if people find out where babies really come from and Puppy Co. has a similar situation regarding puppies. There'll be a story where someone or something threatens both secrets and the two companies will join forces. The babies will call it a joint venture.- IDK about a sequel, but there's a series planned now that seems to be pitting babies against kittens.
Eugene Francis is actually Francis Francis's father
This is already suggested when Eugene promises to "raise him right this time", but the movie drops small hints as well. The biggest one being that, during the pop-up book flashback Eugene is shown already grown holding Francis while his older parents are behind them. It's possible either Francis was adopted (or a doorstep baby in the country-setting) by Eugene, but only if baby corp. Is a meotphor for adoption(at least in the US adopted children can come by taxis or social workers cars), But alternatively it's also possible Eugene just fathered him young, and if so the result is that Francis's legal parents were Eugene's.Also, Francis E. Francis could easily stand for Francis Eugene Francis. Tim has a Fantasy Prone Personality.
As a child, his imaginings made sense, but he's still shown to remember events as wild daydreams even as an adult, as implied by the end of the movie. What's more, one cause of this lingering into adulthood is having parents that readily indulge in the child's fantasies, which Tim's are readily shown doing before Boss Baby enters the picture. You could also argue that there was a hint of cause number 3—loneliness—after Boss Baby entered and Tim began feeling neglected. Tim Wanted a Puppy
Let’s assume the movie is the result of a Unreliable Narrator and a father comforting his nervous daughter. Then the Baby Co./Puppy Co. plotline came from young Tim wanting a puppy more than a baby brother. But his parents didn’t want to juggle a new baby with a new puppy. By the time Tim came to love his brother the desire for a puppy was gone.