Mine is in as issued condition except for the rechambering to .32-20. I have seen one other one that was rechambered for .357 magnum, I don't see why .32-40 wouldn't work. Offhand, the thing I would be concerned with would be overall cartridge length geometry when chambering. If the cartridge is no longer, or a bit shorter than the breech (falling) block, it should work I would think (?). It would have to be short enough to match the curve into the chamber.
They're fun little rifles for sure. According to Cartridges of the World, .32-20 will also chamber .310 greener and a few others in .32. Enjoy yours and good shooting!