Networking / Cold Emailing for Mid Level Roles

The title just about says it all -- any suggestions on how to go about networking for mid-level roles. I've been trying the following, but so far without much success.

• Friend of Friend
• Alumni (undergrad or MBA) if they exist at the firm
• Bank alumni (again if they exist)
• Similar school (UG or MBA)
• No direct connection

At a number of the funds I am targeting / interested in, none of the above apply, or at least not clearly, and am basically reaching out cold and hoping for a response, but as of now it's been pretty quiet (specifically if not alumni). The people I've been reaching out to are generally at a VP/Principal level.

Basically my email format is as below, tailored a bit more to the specific person I'm reaching out to and less broad than "I want to work in PE" but more specific, i.e. "looking to work in consumer focused growth equity" or that kind of thing.

Dear XX,

My name is XX and I'm an MBA candidate at XX. Prior to starting my MBA program, I worked at XX Bank and on the investments team with XX in XX location.

I'm interested in moving into a X role post MBA, and I wanted to reach out to learn more about your experience working at XX firm and get your advice on recruiting for roles in the XX industry

It would be great to speak with you over a quick call later this week or next if you're available. I really appreciate your help and look forward to hearing from you.

Best, XX

Any thoughts on how to make the cold-emailing more effective, either through changing of the email wording, or other suggestions? I guess it is a bit of a numbers game and getting lucky that someone decides to respond, since there is no real reason for them to. My background should be pretty strong at most of the funds I've reached out to (top bank, good buy-side experience, target / semi-target UG and MBA).