Back in the late 1950s & 1960s, a number of cadets were imported and, as HistoricBore said, some were rechambered to 32/20 which was a poor cartridge selection because the 32/20 bullet was undersized.

A few were rechambered to 32 Special but the bullet (in factory ammo) was too heavy for the slow twist used in 310 cadets. However, when handloaded with fairly light loads and with bullets up to 140 grains, they shot fairly well.

I had not seen or read of any 32/40 conversions but that would make sense to me.

A number were rebored to 357 and, from friends that have had one, they are fun to shoot and make nice stalking rifles.

The cadet action was used by many as a basis of small varmint rifles. I had a 22 SuperJet built on a cadet action with a fairly heavy 22" custom barrel. It was a wonderful gun.