The short answer is yes, since you can have multiple badges per course and the criteria for earning those can be and almost always are different.
A common way to do this is to choose different activities requiring completion for different badges in the same course. And since activity access restrictions can have dates on them, you can use this to help control activity completion by date, so you can do this over time too.
The long answer is it sounds like the underlying problem you are trying to solve is how best to build the completion for recurring content over time. The most common solution is to make a separate version of the course. But, there's no one right answer to that; which approach is best depends a great deal on the details of your site and situation.