In some Wharton courses, professors allow students to choose from a set of assignments. For example, perhaps each student is to write up one case, choosing from the set of cases that will be discussed during the semester. Often the due date for this type of assignment depends on when the material will be covered in class. There are currently two ways to set this up in Canvas.
Create an assignment without a due date and rely on the submission timestamp to determine whether or not the assignment was submitted on time. To help identify submissions, you can include instructions in the assignment description that tell students to preface their submission file name with an identifier of some kind - whatever would help you tell the assignments apart. If you download all the submissions in a zip file, you can then sort on the file name. Obviously, this method relies on students following the naming convention properly, so there's some room for error.
The other option is to create multiple assignments with specific due dates, so that it's easy for you to identify submissions. Students will still see on-screen reminders for all the possible assignment due dates, so it's recommended to make the "user's choice" part as clear as possible in the assignment description.
The disadvantage with this option is that each assignment will create an entry in the gradebook. Therefore, you will want to group the assignments together in an Assignment Group which is configured with a grading rule to drop the lowest X scores (e.g. drop the lowest 3 out of 4 scores, if students are to choose only 1 of 4 assignments).
For the best results, apply a default grade of 0 points before you begin grading these assignments. If you don't do this, Canvas might not drop the assignments you want it to drop. Canvas tries to drop the lowest scores, and when it doesn't have a score on an assignment, it ignores that assignment and focuses on assignments that do have scores. This can result in a situation where assignments with grades get dropped, which may not be what you want.