Charlottesville Virginia

My condo steel entry door, 35.75 w * 79.25 h, is half an inch too long to accommodate a new ceramic tile floor in my 25 sq ft foyer. I've been told the door is hollow.

1) Can I shave off 3/4 of an inch from the bottom of the existing door to get the clearance needed? The metal threshold has screws in it so it's not part of the frame. Can the threshold be shimmed under the plate if height build up is needed ?

2) How much should a custom replacement door 3/4 inch shorter, cost if that isn't possible?