what do you mean you will get a degree in May/June? Your first 12 months of OPT should be based on post-completion of a STEM degree. So you were not STEM, or was not graduated and the current OPT is pre-completion OPT? Or you switched I-20 to a degree program after you have STEM OPT? If so, and the second degree is a higher degree, you can get another 12 months of OPT (which is not OPT extension.)
You can try, but your might have an eligibility problem.
