Do you really mean “another” retake?
If you have taken the exam once, you ask for a retake - that’s your second attempt at the exam. This is quite common in many colleges, etc.
If you’ve already had two goes you DO need to ask for another retake. That would be your third attempt at the exam. In most colleges, etc, this would not be done, which is why we are querying your concept.
Also, there is a range in terminology, and perhaps you want an AmE term as you are in the Philippines?
In BrE, resit is normal. We also talk about referral exams, and in my time people clipped the word and talked about doing a re during the supplementary exam period.
Referral – The term Referral is used when you have not met the pass criteria of a module and have to undertake re-assessment before the start of the next academic year in order to progress to the next stage of your course or gain your final award.