People have successfully rooted 4.3, and installed custom recoveries. And, I think. installed custom ROMs. At least on the Sprint version. The same techniques
should work on a Virgin S3, but I don't know if anyone has done it yet.
A couple of cautions: (1)Rooting
WILL trip the warranty bit in Knox. Unlike the flash counter, there is no way to reset it, and probably never will be. This won't affect functionality, but you won't be able to go back to stck and pretend you never rooted.
(2) Don't ever try to use Odin to go back to a pre-4.3 ROM. It
WILL hard brick your phone.
For procedures that have worked for Sprint phones, see the thread below. I do not know whether these will work on a Virgin Mobile phone, nor whether they might cause problems or even brick your phone. I am not responsible for anything you do to your phone. You are completely and solely responsible for anything you chose to do to your phone.
http://forums.androidcentral.com/sp...-hacks/337722-possible-method-root-4-3-a.html
Edit: One person reports rooting a Virgin S3 on 4.3. You might want to PM tem to see how thsy did it:
http://forums.androidcentral.com/sprint-galaxy-s-iii/339257-sprint-galaxy-s3-knox-2.html#post3311754