I have received C band for consecutive 3 years. My grade is BPO2. Is there a way I can be promoted to BPO3? Any steps I should take?

Resign

For promotion they check your last 2-3 bands if you significantly improve then you might get promotion

Are bands out?

Unfortunately there is no way for promotion considering your last 3 bands

Firstly your manager seems in no mood of promoting you to the next grade.
Despite no promotion, you are getting C band every year, either switch company or project asap. Its high time now. I have seen 16 years experienced in tcs as bpo2. Don't think based on your tenure they upgrade your grade.

@TheVillain resignation is the only option