PERM filing / GC initiation without employer sponsorship

[Indian citizen]

I am on H1B visa since the last 4 years and I wanted to apply for GC through my current employer (large IT/BPO US based company) who are very good with such requests and processes. However recently we received a notification that they will no longer support eb2 / eb3 category of GCs. They are only going to process GC applications under eb1 category and I dont qualify for eb1. Please let me know if I can file for GC on my own through a lawyer, considering I can get some kind of experience letter from my current employer.