If you want to get into PE you would need more broad HR experience (retirement plans, equity plans, compensation, labor relations / compliance) or more broad insurance experience (P&C, workers comp, experience with captives) or have connections (probably most important) or an MBA from a top program.
You could switch to one of the Big4 accounting firms or similar (Accenture, FTI, etc.). They have HR M&A groups that are more broad than just H&B - you would probably get a salary bump if you go in as a Manager in a HCOL area.
I’ve been in HR consulting for about 15 years and I’m looking for the exit - better opportunities in other fields with higher comp potential, imo
I’ve worked on a lot of HR M&A projects and, at the end of the day, HR is an after thought in most organizations and it doesn’t get anywhere near the same consideration as finance or IT or operations.
Far better off to put yourself in a position where you can interact with the C-suite on a regular basis instead of benefit managers or Total rewards leaders (or the CHRO if you are lucky)
Just my 2 cents as someone actively trying to make the switch