Assigning multiple due dates is available in the settings for graded assignments, discussions, and quizzes. There are some key points to make note of when using this feature.
When adding multiple due dates, be sure to always use the +Add option under the Assign To box in the settings. This will create a separate Assign To box where you can assign the selected student(s) the different due date and availability period. Once you assign students in the second Assign To box the first Assign To box will change to Everyone Else. Please note if you have an assignment where most students have submitted the assignment and you remove everyone from the first assign to box to pick selected students, only the selected students will see the assignment and grades! DO NOT DO THIS! This causes mass confusion for your students who have previously completed the assignment. They will NOT be able to view the assignment or their grade for the assignment.
If you are assigning the assignment to individual students, you can remove everyone from the "assign to" box so you can select the students who will be assigned to the assignment. You will be warned that the assignment is not assigned to a section. Just click Continue. Be aware only students assigned to the assignment can be graded for the assignment in the grades and students will only see the assignments they are assigned. Please note this is best done when creating a new assignment. As mentioned in the previous paragraph, removing everyone in the first assign to box in assignment settings with an assignment that has previous submissions is NOT optimal and can lead to student confusion.