Houston- we have a problem.....
.22 LR and .22 Magnum do not have the same exterior diameters. A chamber that will accept .22 magnum will cause a .22 LR case to split. .22 mag chamber- .243 22LR chamber-.224. The magnum also needs a slightly larger bore diameter (and uses jacketed bullets). Difference in diameter of the cartridge? .22 LR has a heel seated bullet- bullet and cartridge case- same size. .22 magnum, bullet loaded inside cartridge case- case must be larger in diameter.
There are REVOLVERS with multiple cylinders that do OK- and the Rossi is a revolver. The single shots, such as TC, you simply change chamber and barrel in one.
But as far as an auto, bolt, pump, or lever- no. The energies of a .22 mag are also much greater that .22 LR, and would generate problems in cycling an auto without changing to a heavier bolt, stiffer springs, etc.
This is not a .38 Special/ .357 Magnum situation, where power and case length are the only differences.