Network with MDs Friends?

Hey guys, this might have been answered before but I think this is a situation that is perhaps different from other people's situations. So, I work at a boutique tech IB firm as a summer analyst and the MDs that I work for our really well connected in the Bay Area. As in they know the Vice Chairman for the Tech group for a BB, knows the most famous tech banker in history, and connections to all the MDs & VPs in the Bay at the major firms (Lazard, MS, DB, etc.).

They wrote in my contract that they won't write a letter of recommendation as part of the contract to work for them. But would it be possible to ask them more casually about letting me talk to their friends at the major firms? I've done good work so far and I even got an extension for my contract so would it be a stretch to request for help in the networking process for junior SA?

I just don't want to come off as expecting to receive such support but I just wished I could leverage my experience there to network with more people than I am currently able to get in touch with. Any advice?

Would appreciate it if people can shed some light on this.

Thanks.