There is a very crucial point, why you shouldn't start to invent such requirements.
The idea of unit tests is that each test ... tests a different aspect of your class under test. Aspects that are independent of each other. That is the one side. The other is: unit tests exist to help you to determine problems in your production as quickly as possible.
Meaning: when all of a sudden, a unit test is failing (because somebody changed something somewhere), then you want to find the root cause of this problem as soon as possible. Anything that prevents you from getting to that goal makes your unit test less valuable to you!
Things that make it harder for you to find the foot cause would be:
- extensive "externalized" setup - when you start using (too much) inheritance for your test cases
- complicated relations between your test methods (like: your idea)
Long story short: unit tests are not meant to be run in any specific order. So, instead of spending a lot of time pushing JUnit into a corner where it doesn't want to be ... step back for a second, and reconsider why you think you need things to be that way.