Q: Can I pile up my Keepers in play in a stack, or do I have to lay them out so they are clearly displayed?

A: While it is not specified in the rules, the intention is that all Keepers and Creepers under your control should be visible to your opponents at all times unless there is some specific situation that lets you stack or hide them. In general, if a Keeper or Creeper is hidden under another card, it is as though it does not exist on the table, and a player may only stack Keepers/Creepers in certain very specific situations.

For example, in Martian Fluxx, you are allowed to hide your Pathetic Humans (Creepers) under your Abduction Chamber (Keeper). They are effectively “not showing on the table” and do not prevent you from winning (though you can release them at any time to meet a win condition).

There is a similar card in Pirate Fluxx that lets you hide your “booty” Keepers under your Treasure Map. They don’t count towards the Keeper limit, and this protects them from being Plundered, (a special Rule in Pirate Fluxx) but if someone uses Steal a Keeper to take your map, they also take the booty you’ve hidden under it.

In Cthulhu Fluxx, one may hide one Creeper under the Elder Sign card, which neutralizes it, much like the Abduction Chamber does for Pathetic Humans, but for only one Creeper.

There may be other cards which allow similar situations, but unless you have any of these special cards that allow you to hide a Keeper or Creeper in front of you, all your Keepers and Creepers need to be showing. If space is an issue, you can overlap them so the name stripe is showing, but you may not simply hide them from the other players.