Sifting litter box idea
 

The main part of the box would be made from the same plastic and process
that Sterilite uses for their clear smooth plastic boxes.

I think it would require three boxes, or two boxes per area plus one
roving box.

Every box would look like a standard litter box with tall sides depending
on your preference.

The bottom of the each box would be solid on one side (like an ordinary
litter box) and sifting material on the other side like the bottom of the
sifting box out of the "Van Ness Sifting Enclosed Pan" set up.

https://www.youtube.com/watch?v=Fm1uvWO7inI

Only half of the bottom of each box would be sifting material. The top box
sifting material would be on the left half of the bottom. The box
underneath that would would be turned so that the sifting material is on
the right half of the bottom.

That way, when you have at least two boxes stacked one on top of the
other, alternating direction, litter will not fall through.

You would have to pick up the litter box combination (two boxes) and set
them into another box. And then sift by removing the top box.

You could use a single roving box and just turn it in the direction
necessary (opposite the direction of the bottom box) before placing it
under the bottom box.

What's the benefit? No need to pour the litter from one box into another.
Majorly cuts down on dust. And it's easier even though you still have to
pick up the litter box, that operation is just up and down into another
box.