Federal limit on a tridem with out a permit is 42,000 if it has a 10 ft spread it goes to 43,500. Some states may allow more but usually not on interstates. If your permitting weight then most standard is 20,000 an axle but again some states may allow more.
Unless your getting permits the tri doesnt get you any more weight than a spread pair. It also seems to take up the same space. The only situation that makes sense is when you have the small tires that are a low load rating.
Some states is 42K all the way up to 51K (IN)... LA will allow Non-Interstate highways: Single 20,000 Tandem 37,000 Tridem 45,000.... 80,000 Gross (with a Tridem axle, 83,400 on Interstate & 88,000 non-Interstate if licensed for it)
Also be aware of your kingpin setting and most of all, updating your IRP to have the privilege of hauling heavy and trust me they do check, some states won't issue a heavy permit without proof of your heavy IRP