EB greencard help

[immigc2009]

I work for company X on h1b. I have MS degree from US, however they want to do EB3 filing. There is also a company Y who is willing to do EB2 GC filing for me. My question is, if company Y agrees, can I request company Y to start my GC process without me leaving company X? Do i have to notify compnay X (my current employer) about this process. My plan is to join company Y after approval of GC. I am looking for suggestions.

Thank you

[txh1b]

GC is for future employment and you need not be working for the company. It would help if one is working by the time a I140 is filed so that any ability to pay issues can be handled appropriately if one is already working and getting paid the GC salary.