I propose...

...making a short piece of film showing multiple views of a simple object which can be found in the space in which the final film will be exhibited – the light switch for example. For the exhibition, the film will be projected onto the original object.

The film will be constructed by filming the object from one viewpoint, then reshooting it from another viewpoint whilst the first film is projected onto the object. This process will be repeated five times so that multiple viewpoints of the object are overlayed on the single piece of footage. Whilst most of the viewpoints will be shot using a tripod for the camera, one may be shot handheld to provide a certain amount of variation. 

At the end of the film the projected image will go to blank, before starting again. 

The final film will be projected onto the original object in the normal light of the exhibition.