You need to have a valid nonimmigrant status to remain in the USA. If your purpose is to continue education, F1 is the visa to go. If you are in the USA and have I-94 for D/S all you need is new I-20. Talk to the DSO
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1). Yes, you do, since the MBA will be yet another degree, separate and distinct from the MS which you already have.
2). Yes again. The completion of each degree entitled to an additional/separate OPP or CPT. Make sure to talk to the academic institutions DSO about this in order to get more detail and information.
3). See my answer number 2 above. First identify the school in which you want to obtain your MBA, then go and speak with that schools DSO and or foreign student advisor about your plans.
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