You sure can! I did just that. Put a 7prc proof barrel on a 300 WM tikka action and had planned on doing it with a 300WSM action. You will just need a Winchester magnum magazine and a longer bolt stop for the longer cartridge and you are GTG. All t3/t3x are the same length. Only thing that changes action wise is the bolt stop, magazine size, and bolt size(cartridge).
This is the same magazine as the top one above for less. They also have a 5 round that is the same and they both have a little better COAL than the factory mags.
Tikka T3 / T3x DBM for factory magazines - Titanium and 7075-T76 alloy
lumleyarms.us
These are all the parts I used and researched. Had tried to go through JA outdoors and they wouldn't give me the time of day so I found better products or the same for cheaper through the two I showed.