.38 Super is nominal .384" O.D., .357 Mag is .379".
Depending on tolerance overlap a minimum Super cartridge might chamber in a maximum .357 Magnum cylinder, or it might not; same as .38 S&W in a .38 Special.
When it does, I have seen reports of fired cases sticking tight in the chamber.
Don't do it.
S&W has made some true .38 Super revolvers with correct chambers and magnum heat treat cylinders. They load with moon clips to avoid the risk that the extractor might not pull the empties by their semi-rims.
There is at least one gunsmith who will convert a .357 to take a number of rimless rounds on moon clips, 9mm, .38 Super, and 9x23 Win.
I would expect oddballs like 9x21, 9mm Largo, and 9mm Steyr to work, too.
But then the .38s and .357s will stick in the tapered chambers.
He will convert a late model .38 Special to take 9mm P only.
http://www.pinnacle-guns.com/revolver.asp