I think what needs to be done is copy from colleges. Colleges and universities know how to network among their alumni.
They have people whose sole job it is to keep track of Alumni. They invite the alumni to events and solicit donations from them.
One differnce though. I dont know why this is, but in the academic world, they try to solicit for the endowment. Very few yeshivas have endowments or try to solicit for one.
In a university a chair is endowed for example. One person donates enough money so the salary of a professor can teach a course.
I dont know why in yeshiva, a person could be endowed to learn all day