There is no functional problem in converting
any of the M14 guns in any of these calibers:
22-250
243 Winchester
260 Remington
7-08 Remington
338 Federal
358 Winchester
450 Marlin
However, with some of the above chamberings,
the action will have a quite limited life expectancy.
Other 308 guns with stronger actions can handle other cartriges as well.
AR10 was tested with all of the above plus a sh!tload of others,
some of them I don't even know what they are
(6.5 Creedmoor, 338-7mm Benchrest, and all kind of other oddities).
FN FAL has been tested many years ago
with cartriges developed by FN Herstal.
G3 was tested with a large array experimental cartriges
developed by Norma and Lapua.