Should I negotiate an offer with a "fundless sponsor"

Hello all!

I am an investment banking analyst at a MM and recently got a verbal offer for a new role which I am happy about since I really want to get out of IB/my team. The title reads Corporate Strategy & Development but the job description reads PE/investment associate responsibilities and the team mentioned that they view this as a hybrid role. They also think of themselves as as “fundless sponsors” in that they will reach out to other parties for both equity and debt financing which is a little confusing. They also seem to be a family office but perhaps without a fund/AUM given their “fundless” status.

Anyhow, the offer is on par comp wise to other Corp dev roles but very low compared to say a small family office investment associate role. Given the hybrid nature of the role, I spoke with my network in PE (mostly junior and one senior person) and they suggested I 1) carefully ask if they can up the base especially as their is no 401k match / the offer is kind of low if there is a PE component / there is no harm in asking and 2) Ask if I can start in two months when my bonus is paid out (stub bonus though)

I feel comfortable asking for the second but am worried they would rescind my offer if I asked for more money. I’m also a little confused as to how to view the role, should I be paid for a little more than a corp dev role and a little less than a LMM family office PE role given the two comp points? Any insights would be appreciated - I do intend to sign even if I get neither request.