Unfortunately I don't believe this is possible natively. However, a custom entity could be used to contain all the tasks related to a particular related entity. You could then expose that through a sub-grid on the original record. This could complicate things
a little bit with reporting if that's a concern.
You could also create a custom task as a "master" task type, and then track high level activity in there. I don't believe there's a native way to then parent that custom task to sub-tasks however.