This information is readily available on the OOTB Process Tab in the Process Status Table where Users can see the name of the assignment, the assignee, the role of the assignee, Vote, Comments, and completion (By, Due Date, Date Completed).
If at all possible I would recommend leveraging this OOTB capability as to have this information appear in the Users Tasks Table would require some non trivial work. What shows up in the Tasks Table is a Work Item and everything you see are attributes of the Work Item Object. The preceding assignment would be a different Work Item Object, linked to the same process object. You would have to add attributes to the Work Item and develop code in the workflow (process) to pass information from one to the other. Doable, but why when the information is already visible elsewhere?