First, I understand JUnit is fundamentally a unit testing tool, but I hope I can achieve what I want with JUnit.
The tests I am writing with each test case acting more like a test step (at least conceptually). There are particular blocks of these steps that I would like to make common as they may fit into other work flows (yes, this is functional testing…).
Is what I seek possible?
If I understand you correctly you would like to introduce an interdependence between the unit tests. I think that this is most probably a bad idea as the unit test should be able to be run in any order and/or just one at a time. Introducing some implicit required order in your tests seems like the wrong path to take. If there is some process to follow then each test should be able to perform that process in isolation.