Hello Thomas, thanks for your question.
The main question you would have to answer is: Given your career goals, what would an MS Finance give you that an MBA would not? It is critical to demonstrate to MBA admissions committees that your desired career path necessitates business school. So, it is not an outright dealbreaker to have an MS in Finance when applying to business school, but you would have to be specific about what you would get from an MBA that you would not get from an MS. That would beg the question of why do you need both.
If you have clear and logical answers to these questions, then fine. But, I would not apply to both without first knowing your reasons.
Best of luck,
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