Lots of private jet operators, you could also get a VP-B / VP-C / VQ- / M- validation for your license and fly a bizjet in Europe with a FAA license, but...
a.) these jobs are basically never advertised, it's only about knowing people in the business
b.) you'll need plenty of jet hours for those jobs, def. not low-time material
c.) it's just really all about who you know.
To sum it up, your chances are higher (actually low, but not as low anymore
) if you'd convert to a JAA license.