You can work on any foreign flagged vessel that will hire you. You’ll need a CoC from the flag state under which the vessel is registered. Generally the company will submit the application on your behalf with copies of your US credential and STCW. The CoC is that flag states document saying your home state license (USCG + STCW) is equivalent and acceptable.
Whether or not a foreign company will hire you is a different story. Some nations have restrictions like ours. Even oil patch companies that will hire you on foreign flag vessels may not be able to place you long term on vessels overseas depending on country and sailing position.
Your assumption about pay is just that, an assumption. I made far more sailing foreign flag than US flag, especially overseas with tax credits. But I can’t speak for foreign flag general cargo vessels.