You can apply for the H-1B without an impact on your STEM. You will file your H-1B as a change of status from F-1 to H-1B. Incidentally, with the H-1B you don't need STEM as you will be eligible for H-1B Cap Gap which will extend your OPT from June 20-Sept 30, 2012. All you need to do is provide your school's Int'l Student Services office with a copy of your H-1B receipt (if filed before June 20) and have SEVIS updated and your Form I-20 updated. This will automatically extend your OPT through Sept 30. Your H-1B will be valid Oct 1, 2012. However, since you've already filed the STEM it will provide extra protection in the event of an H-1B denial or RFE.
Have you talked to your DSO? You should be ok, as your H-1b will not kick in until Oct 1 if your employer is subject to the cap and your Stem extension should be approved before that time.
do you have a lawyer helping you?
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I agree with my colleagues.
You should discuss this with your DSO or with the attorney that is going to handle the H-1B filing. If you do have an employer, you should have him file the H-1B as soon as possible.