Originally Posted by
DropYourSocks
Visa doesn't transfer, but you can actually hold multiple E3s. So you get an offer from a new employer, get the appropriate paperwork, go to consulate appointment, reenter with 2 visas, start new job when ready.
You can't work for 2 companies fulltime on an E3. You can work part time for a second company and that's it.
If you apply for a full-time position at a new company, your old e3 will be cancelled (if your previous position was fulltime) when your new one is approved.