Flagstone breakfast room floor: how to seal, protect and yet have shine? Can a sealer go over impregnator?

Q. 25 years ago our painter put some kind of sealant epoxy, polyurethane, acrylic, something like that on a new flagstone interior entry. It‘s held up beautifully. We are about to install flagstone in a small breakfast room. We want to retain the color of the stone, have an hard, protective surface with some gloss, much like we have in the foyer. Most of what I read advocates an impregnator and I gather they don‘t change the smoothness of the surface or allow shine? Can we put a high solids or resin coating over an impregnator? What would you suggest to get close to the results we want? Stone is here, waiting to go down, and we are stumped!! Including our stone mason!