Using rear screen projection that way is a fairly common concept. The biggest problem is usually finding the room required.
Short throw lenses can allow the projectors to be about a screen width behind the screen (e.g. about 12' behind a 9'x12' screen) but these lenses also require the projector to be mounted online with the center of the screen both horizontally and vertically, there is usually no lens offset possible. Going to a lens that allows more flexibility in the projector position typically requires at least 1.5 times the image width or 18' of depth (plus the projector depth) for a 12' wide screen. The depth required can be reduced with mirror systems but this adds cost and complexity.
Now add that you don't want projectors interfering with one another or light leakage from one screen to another and the power required. Also consider how the screens and projectors will be physically mounted and the potential of damage to the screens. You would also need to consider how you control 3 or 4 screens, unless you have an exceptionally high contrast projector and screen you would want to mute or even better gate the projector when there is no image to be shown and then unmute it when an image is desired so some remote control is probably required.
Also remember that with rear projection you might be pretty brightly backlighting your characters and can even cause shadows with them, so more front, side and key lighting might be required to overcome the light from the projectors. At the same time, although rear projection is much less susceptible to ambient light, you'd still like to keep the light on the screens to a minimum. These lighting issues are why you often see screens used for backdrops set back some distance from the actors.
Not trying to discourage you, just noting some considerations that often limit whether this concept can be effectively implemented. In many cases, the space available simply doesn't permit this approach to work very well.