As an example: suppose you have a personal project like Angular Seed (which is a starting point for an Angular project https://github.com/angular/angular-seed).
Now
I think the right answer here is to use something like Yeoman Generators. (http://yeoman.io/) You want to use the git repo with your seed project as a generator. It wouldn't allow you to continually pull in changes from the seed project though.
The solution of using two remotes works, but eventually the projects will diverge enough that will make keeping those projects in synch very difficult.