First, you can't rechamber to a round with a different bullet diameter. For example, you can't rechamber a .30-06 to .35 Whelan or .270. To change bullet diameter, you have to rebarrel.
You also must rechamber to a cartridge that is larger in all dimensions than the original cartridge. You can't rechamber .30-06 to .308 Winchester, for example, or even the reverse, since .308 is larger at the shoulder than .30-06. You can't rechamber to a cartridge longer than the magazine. You can rechamber .30-06 to something like the .308 Norma Magnum, which was developed for just that purpose. Some rechambering/rebarreling may require bolt and/or magazine work, which adds to the cost.
If the prospective case is shorter, you can have the barrel removed, re-threaded, and set back. That will work OK on sporter barrels, but not on some milsurp barrels if the original confuguration is to be retained. (For example, setting the barrel back may mean the bayonet no longer fits, or the sights are off to one side.)
Jim