Switch Employers while H1B appeals still pending?

[Meng2s]

So my H1B appeals is in AAO. And I am working on CPT while that is pending. I applied in April 2013, and notice for application being moved to AAO came on Feb 2014. I am really dis satisfied with my current employer and I wish to switch to this company X which is way better. So while I am on CPT, can I change my employers, and if my petition gets approved after I join this new company, would I be able to apply for transfer then?

Also, does anyone know if there's a way to follow up on the case? I was supposed to know my decision within 6 months and I have less than a week left.