There's "can't," and there's "shouldn't." I hope we can all agree that the best advice is to only shoot through any firearm the ammunition it was designed for. Yet, with that said, one of the attractions of the .327 Federal Magnum is that guns chambered for that can also
safely shoot two or three other .32 caliber rounds of less potency. We also know that guns chambered for some of the VERY hot .45 caliber wildcats can also shoot .45 ACP, even though the chamber is too long, simply by headspacing on the extractor. It's not recommended for a lot of use, and probably doesn't achieve best accuracy, but it can be done.
But as for the 9mm Largo and some of the alternates, it ain't that simple. The .38 Super (and the .38 ACP, which used the exact same case) is a straight-walled cartridge. All the 9mm cartridges that might be considered here are tapered. The 9mm Largo has a base diameter of .389", tapers to .377", and has a body length of .905". The 9mm Luger is also a tapered cartridge, measuring .391" at the base, .380" at the mouth, and a body length of .754".
Although the 9mm Luger is shorter, it's also fatter. If a gun chambered for 9mm Largo has a tight chamber, 9mm Luger may not chamber at all. I know for a fact that 9mm Luger won't chamber in a .38 Super barrel -- but that has a tighter chamber than 9mm Largo. The .38 Super cartridge is .384" in diameter x .900" long.
This suggests that .38 Super (or .38 ACP) could probably be fired through a 9mm largo pistol, if the extractor will hold the rim in firing position and if the chamber throat will accept the larger rim.
One last alternative that hasn't been mentioned is the 9x23 Winchester. This case is also tapered, .392" at the base, .381" at the mouth, and .900" long. This one should chamber in a 9mm Largo unless the chamber is unusually tight, and I have read reports of people who use the two cartridges more or less interchangeably. But ... as always, be VERY aware of pressure, and don't shoot high-pressure loads through older guns that may not be built to handle such pressures.
[Diagrams from Steve's Pages
http://stevespages.com/page8d.htm ]