Multiple Travis PR checks with different configurations

In Mark a build "passed with warning" when "allow_failures" jobs fail, @adrienbernede asks:

Would it be possible to have 2 (or more) lines of feedback in Github from a single pipeline in Travis, maybe 1 per stage or configurable? This way I could for example get an independent feedback for my “optional” stage.

I’m pretty sure it’s not possible “from a single pipeline” but I do see multiple Travis checks from different pipelines in some projects – e.g. a “branch” build and a “PR” build. But don’t know how it’s done and how customizable it is.

The intended use case is to track various stuff in PRs separately from the main “test pass/fail” as non-required checks. Post 3 in that topic has examples.