Shower Drain

My shower drain has a 4" cover plate attached with two 10-24 ss x 3/8" machine screws. It is a PVC type drain but has a mild steel insert for the two machine screws. The inserts have completely rusted away and I have removed the screws. Any way to repair without removing the tile and floor and replacing the entire drain? Could I rotate 90deg and drill two holes in the pvc and reinstall the screws into the pvc? Or drill deeper into the pvc and install 2 new 3/4" long screws in the existing position? Any ideas appreciated, Thanks
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clean area, apply bathtub caulk in a couple places, to hold the drain cover in place
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