Obtaining something like a "renderbox"

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I am working on a sci-fi project, and we want to obtain a certain effect.
Having a character levitate some kind of hologram above a desk, hologram in the shape of a box, like a cubic screen.
And inside this cubic hologram display, zooming on certains parts of a 3D model.
while the cubic hologram remain at the same size on the desk.

The thing is, the concept seems like basics sci-fi stuff, but we have absolutely no idea how to obtain this effect in 3D.

We thought of Bolean meshes, but the bolean way of "cutting" objects is not dynamic.
Or to fake the effect using a DepthofField map, but it would only help us haide background object, and not frontground.

The ideal would be to have a "render box", a box in the scene where everything inside is rendered, and everything outside is not.
The hard part is also to have the meshes "sliced" and not just hide and unhide.

Would by any chance any of you know a way or if it's plainly impossible?

At this point we are using Maya and Octane Render, but we're open to switch to any software or render that would make it work.