You can configure multiple due dates/quiz start times for any item you can assign to a student.
This applies to Canvas Quizzes, Discussions, Assignments, and more.
Click on the item you want to add a due date to.
When viewing the description, click on "Edit"
Then scroll down to the "Assign to" area. By default, Canvas will create one "Assign to" section. In this section, you can change who the item is assigned to. Type their name or group.
If you would like a second due date, click the "+Add" button, and you'll see another "Assign to" section.
If you add a second due date, and add people/groups to that due date, the first due date may change to accommodate. In my example, I left the first due to assign to "Everyone", but when I added a student to the second due date, it changed the first due date to "Everyone Else".