Yes, that is possible. The trick is to let your unit class test hierarchy follow the class hierarchy of your code.
Let's assume you have an interface Itf with implementing classes C1 and C2.
You first create a test class for Itf (ItfTest). To actually exercise the test, you need to create a mock implementation of your Itf interface.
All tests in this ItfTest should pass on any implementation of Itf (!). If not, your implementation does not conform to the Liskov Substitution Principle  (the "L" in Martin's SOLID principles of OO design)
Thus, to create a test case for C1, your C1Test class can extend ItfTest. Your extension should replace the mock object creation with the creation of a C1 object (injecting it in, or using a GoF factory method). In this way, all ItfTest cases are applied to instances of type C1. Furthermore, your C1Test class can contain additional test cases specific to C1.
Likewise for C2. And you can repeat the trick for deeper nested classes and interfaces.
References: Binder's Polymorphic Server Test pattern, 
and McGregor's PACT -- Parallel Architecture for Component Testing.