If it is an International Match rifle, not one of the Mk's, then it may be possible. The International Match rifle (some call it a Mk I but BSA never did) would have the plate like extractor that may be modified to accept a 32-20. Later models had an improved extractor and the rear of the barrel around the chamber was a raised lug, not much wider than the .22LR rim which would be difficult to make a 32-20 case fit.

Not many successful centerfires have been made on the International platform that I have heard about. A better action would be one of the small frame BSA actions. There a 32-20 is quite doable.

Had BSA international made into a 32MS  a number of years ago.  weak moment and sold it.  now having another built in 32  and should see it this summer sometime.  must use a hand push breech seater to seat the bullet.  but I am working on a mechanical at present.  not pretty but should work  barel is in 14 twist douglas  and shot a 210 gr bullet 

will post picture when it is all done latter this year