According to the SAAMI dimensions, the shoulder of the 32-20 is slightly past the end of the 32H&R mag case, so it should work. Alternatively, if possible the barrel could be set back. If the firearm is a revolver, the cylinder might not be long enough to handle the 32-20 round.
An alternate to the 32-20 is the 327 magnum, which is a longer yet version of the 32 S&W family of cartridges. It can give performance equal to the 32-20 in a firearm capable of handling the pressure and has the advantage of allowing any of the other 32 S&W based cartridges to be used in the same gun.
