Can't you have a pet slug instead...

HAHA ! So wait, I learned that the accusative object of a verb takes the genitive form if the verb is negated. But here it's even trickier because the modal verb is negated, and not the infinitive, which governs the accusative. But still the accusative has to turn into the genitive. Madness is upon our heads.

What's the plural for monkey?

Why do you correct me? (You can`t have a monkey)

you can have no monkey