In Blackboard's Test Options you can select certain students to have multiple attempts, a longer time to completetest or change the availability date in the Test Availability Exceptions section of the Test Options:

Instructions on getting to the Test Availability Exceptions section of a test's options

1.  In Blackboard, on the left side panel, go to:  Course Tools > Tests, Surveys, and Pools > Tests 
2.  Here you will see a list of your tests.  Click the drop down arrow next to the test you want to modify > Edit

3.   Click the drop down arrow next to the test name on the top of th next page "Test Canvas:  [yout test name]"  > Modify Options

4.  Scroll down to  Test Availability Exceptions and click Add User or Group, then add the students to provide them with a specific number of attempts, time or change the date the test is available to them.

5.  Click Submit when you are finished.