I think its perfectly ok to use a base test class for your common code and then extending that in each of the Test class. In fact the test strategy should be in-line with the design of the project code. I am sure that your project module would have some common code as well, your common test section basically map to those functionality of project code.
I have done similar design in couple of projects without any issue.
So, whenever your project has a change in common functionality, it would affect test case in common test class, while specific changes go with specific test class.