A: Yes. In Star Fluxx, you could have an Evil Malfunctioning Robot. In Cthulhu Fluxx, you could have a Metamorphosing Poet who is plagued by Nightmares.

The only exception to this is in Anatomy Fluxx, where, the way the Creepers are written, you can only attach them to a Keeper which is not already afflicted, so any given Keeper can only be attached to one Creeper. On the other hand, in Anatomy Fluxx you also have the only case where you can have multiple Keepers attached to one Creeper.
If the Rule It’s Spreading! is in play, then, every time your turn comes around, you must attach an additional Keeper (if you have any unattached in play).