Part 135 Cargo Payload Limitation

[ANTI-ICE ON]

Greetings and Merry Christmas to all.

Not sure if this is the right place for this question, so please re-direct if not.

Part 135 states that the airplane used must have a maximum payload of 7,500 pounds or less.

If I got that rule right, how would one operate a heavier (ATR / 737 / A320) cargo aircraft in on demand cargo charter operation in the US ?
Is Part 121 the only other option available ?

Thank you in advance.

[ATPMBA]

Hi, I believe Part 121 would be the path, however, if you are moving cargo for a company that owns the aircraft, example an oil company owns a B737 and use it to fly their own oil drilling equipment then they could go Part 125.
Part 121 requires extra management/staff positions such as a Chief Inspector and dispatchers. Feel free to message me if you want to discuss some ideas.

[B2N2]

This is where 121(S) comes in, Supplemental.