As previously stated limitation is magazine length and bolt face. The 6mm Rem is .473 Bolt face and I am unsure if yours is a long action or short action. Most factory Remington 6MM are on a short action . Mine is on a long action Remington 721. You can just search for .473 calibers and go from there, you will need to know your action size so you don't pick a long action caliber like 25-06 and attempt to put it on short action. Best of luck
I did one to a 7mm-08 and another to 338Fed. You could go classic with a 257 Roberts or one of the new rounds like 6mm or 6.5 CM. One of the fast 22s like a 22-250 or a 22 CM.
Any short action standard bolt face will fit just fine.