Filmic exactly in what way? Many Hal Prince stagings (though not Prince exclusively) are/were "filmic", using "cuts" onstage with precise light changes and entrances. Follies, for example, was staged as a series of disjointed moments. The background music (played by an onstage band and supported, I think, by the orchestra) actually shifted between moments as it might in a realistic film document of a backstage party, switching mid-song as characters appeared here and there on the set.
That kind of visual guidance is similar to one of the most basic concepts in film editing, which is described by Walter Murch as finding the "dot" on-screen that audiences are watching and making sure its path doesn't get muddled from shot to shot.
Visually, as in lighting/equipment, there was a production of three Antonioni films that was staged on a blue-screen with cameras on tracks and big lights, and the audience watched the live performance both on the stage and on big screens above it, which displayed the camera output. I don't know how successful or entertaining it was but you can watch a clip here: https://vimeo.com/80484327