How do I remove the flow restrictor plate from a Moen S6320 shower head? Can I just drill a hole in the green plastic plate?

Yes, you can drill it out. But before you do that, try to remove it first. Take skinny, flat, screwdriver, hook the restrictor, and see if it comes out. You can also try skinny needle nose pliers. Restrictors are pushed in in factory, so they should slide back up. The only trick is to get a good grip

When you drill the restrictor out, you will have some plastic shavings to fall inside the shower head. I suggest, before you reinstall it, flip it upside down and top it several time on a piece of wood to shake the shavings out. Otherwise, they may clog passages or nozzles inside the shower head

Hope that helps

Milo