Yes - but it has to be after the stated date and for a justifiable reason e.g. a clash.
CSSA set a timetable and they can have clashes as they don't have the lines from all the schools that do the papers so they have a clause in their contract with the schools along the lines of 'you have to sit these papers on the day and time we specify, unless their is a clash, in which case you can reschedule the test AFTER the date and time we specified' - it isn't in exactly those words of course but it is the gist of it.
Last year I had two students who had a clash between Hospitality and Extension History - so one of those exams had to be moved as obviously they couldn't do both papers at the same time.
You are also made aware that if a paper is moved it has to be moved to a later day and time and that there is a possibility of students accessing the questions.