In D2L, there are two tools to give students more time to complete Quizzes: Special Access and Accommodations.
Special Access should be used for specific activities and one-time situations, such as personal emergencies. For example, let us say a close family member of a student became ill and went to the hospital on the same day as a D2L Quiz is due. Instead of building a new quiz for that student, you can give them special access to the original quiz. You can set it so that they have access to the quiz at a specific date or set it so that they have time from the date you set up the special access until a later date. You can also give students Special Access to a Dropbox. View this video to learn more about Special Access or take a look at the Special Access Text Tutorial.
You can potentially use Special Access to provide a group of students with an alternative quiz or Dropbox assignment as well. In the Manage Special Access pop-up, above the Add Users to Special Access, there is the option to Allow only users with special access to see this quiz/folder. This could be useful if, for example, several students are on a sports team and are going to be missing the quiz. Or maybe you want to provide several different versions of a mid-term or final exam. If you are interested in providing different materials, activities, or exams throughout the semester (maybe because you are teaching a merged course), please contact COLI to discuss this further.
On the other hand, D2L Accommodations should be used for students who consistently require extra time on Quizzes. This can be especially useful if you are contacted by the Student Accessibility Services on behalf of a student to request the student be given more time on all quizzes or exams. Instead of spending time adding Special Access permissions for each individual quiz for this student, you can give this student a D2L Accommodation. You only must give this Accommodation once. D2L will understand this to mean that, if a student does a quiz, they should get an increased amount of time specified in their D2L Accommodation. View this video for more information on Accommodations or take a look at the Accommodations Text Tutorial.
In short, Special Access should be used on a specific Quiz or Dropbox to allow a student that has missed a deadline to access it at or until a later date. The Accommodations Tool should be used to give a specific student extended time on each Quiz or Exam in D2L as dictated by Student Accessibility Services.