I want Jenkins to automatically find and run the test suite for every branch that is part of an open pull request. Is this possible with some Jenkins plugin I have not found?
If you happen to be using Cloudbees, they offer their own pull request builder plugin.
https://wiki.cloudbees.com/bin/view/DEV/Github+Pull+Request+Validation
The advantages they tout over the standard Jenkins Github pull request builder is that it runs as a "tenant-isolate" program, preventing the code in the pull request from snooping around for passwords or ssh keys. I could see this being particularly useful for a public project.