I have an Emco 9x20, and have had good luck with the parts I've gotten from Grizzly fitting, mostly handles, and fittings. There have been a couple parts that had changed, but even these were mostly adaptable by getting the neighboring part, probably more a matter of age than brand. Over time parts get minor redesigns.
You want to look at the Grizzly G4000. They have a good parts breakdown, and I've found Grizzly's parts dept to be easy to use.
Be aware some of these lathes are metric and some inches, at least so far as the spindle thread. Jet uses a 1-1/2"-8 spindle, the current Grizzly G4000 and many of the other brands use a metric M39 thread. Some older Emco and Grizzly used an inch thread. I do not know what if any impact this will have for other parts.
Grizzly G4000 parts