In the normal experiments we perform, the screen is already a classical system, collapsed / entangled with the rest of the "classical world" (depending on the i

In the normal experiments we perform, the screen is already a classical system, collapsed / entangled with the rest of the "classical world" (depending on the interpretation). When the particles interact with the screen, of course their wave function collapses as well. But what if instead you had a screen that was itself a quantum system? You'd then use the Schrodinger equation without any collapse (without the Born rule) to describe the results. You'd have to perform other measurements on the quantum screen to obtain a classical result that can be interpreted, of course. But nothing in QM says that there is some size limit, so in principle it should be possible to prepare a quantum system of any size, including the size of a typical double slit experiment screen, that doesn't collapse.