First attempt at a sink drain screen with a knob that can be turned to close the holes. It's parametric so it can generate any size you need. The parts snap together, but the cap may need a drop of super glue to hold it together. Play with the tolerance variable till the parts slide together well on your printer.

It worked for me, unfortunately it drains very slowly and needs more holes! Even with the blocker removed and the central hole open, it still drains too slowly.