Some years ago, I found what was called a 'candle plate' of 1/4" glass, measuring 9" x 13", at Hobby Lobby. Basically a simple rectangle of glass with finished & frosted edges (bevelled on upward side). Also had some adhesive rubber feet on the bottom side, at each corner. In order to facilitate its use as a backing for a sheet of sandpaper, I removed the adhesive rubber feet from the fully flat bottom side, and replaced them on the upper, bevelled-edge side. This allowed for the plate to be flipped over with the fully flat side to be facing upward, perfectly set up for a full sheet of wet/dry sandpaper to be taped at the ends. Think I got lucky in finding that - I bought two of them at about $5 each. Don't know if they can still be found in that perfectly convenient size. But still might be worth looking for.
Another option I've seen is at the home improvement center. For a time, I was eyeballing some 'backsplash' material in synthetic quartz or granite, used for trim around quartz/granite countertops or vanity (sink) tops for the bathroom. The backsplash pieces were roughly 3/4" thick, 4"-6" wide and maybe 18" long, give or take. Every time I saw those, I pondered their use as a backer for sandpaper. Never got around to trying it though, as my sharpening habits were gradually steering away from sandpaper, toward bench stones.
Yet another option... I found an inexpensive granite surface plate at a Woodcraft store, years ago. They were marketing those to folks looking for a sharpening base (used with sandpaper) for woodworking tools like chisels or plane irons. 2" thick slab of granite, and measuring roughly 9" x 12" or so. And although relatively inexpensive (think I got it for $25 - $30 or so, on sale at the time), they were actually surfaced prepped & spec'd to be quite flat, within a few thousandths' of an inch from corner to corner. This has been my favorite backer for sandpaper, when I've chosen to use it that way.
Still another... For coarse-grit reprofiling, a simple sanding belt (for powered sander), can be cut at the diagonal seam and glued flat to a hard backing, like a board. I've used a 3" x 21" belt for this on occasion. Make sure the belt is in an aluminum oxide grit (most are, anyway). Something like ~ 50 - 120 grit, with the full 21" laid out flat, makes for a FAST grinder of edge bevels.
Once you start looking around, you'll notice a LOT of options for these. Just need that seed to be planted in your mind, and the possibilities will jump right up at you when you're out shopping.
