YOu can do it with a opened up bolt face or a Dave Kiff bolt, however you talk to a lot of gunsmiths, they won't do it.
I own a Rem700P, stock (actually selling it) and I haven't seen any issues, but apparently the diameter of the tenon and the subsequent thinning of the barrel chamber where you thread creates some concern with a cartridge as wide as the Lapua or 378 Wby. It really is the bolt issue as much as that.
Now, all that being said, Rem makes a 338 LM that is used by the military, that goes through a strict compliance test before being even put on the market. But don't be surprised if gunsmiths balk at a project like yours.