I'm new to this forum. I have been doing a little of research into this because I have a Sig 239 in 40 which I can convert to 357 Sig with just a regular 357 Sig barrel switch. To shoot 9mm you need a 9mm CONVERSION barrel which I think has to be bought from a 3rd party vender. You are suppose to be able to use the same mags for all 3 and no spring change. But make sure you get the Sig in 40mm. If you buy a 9mm the slide will not except the other barrels. Also do not buy it in 357 sig because Sig sells that version with mags that only except the 357 round so you will have to buy new mags.
With Glock, a 40 such as the 23 will except the Glock 32 barrel (357sig) and I'm sure other models will do the same. Only the barrel needs to be changed. I don't know about 9mm though. Never check that.