A companion of sorts is Nestflix [0]: "Fictional movies within movies... Fake shows within shows... Browse our selection of over 700 stories within stories."
My favorite "movie withing movie" idea is "Wormhole X-Treme", the Stargate TV-show within the Stargate SG1 TV-show.
They use it for self-deprecating humor, by e.g. lampshading the sometime easy scenaristic shortcut they take, with some episodes where the "real" Stargate SG1 cast would (secretly) serves as advisor for Wormhole X-Treme spoof tv-show.
On top of that, the justification for it is absolutely genius: Because that way, the (in-universe) army could quell any rumor of the existence of the Stargate Command by simply saying "No, that from a TV-show, duh!".