MBA After A Dual Degree In MiF And MiM?

I'm considering getting an MBA after my dual degree in MiF and MiM because I want to migrate to the US. This is the most convenient way for me to establish myself in the states since I'll be able to network and get a job when doing an MBA. My goal is to work in PE so I'll probably look for something in IB to begin with.

What do y'all think? I realize this would be unnecessary under ordinary circumstances but we all know that it's practically impossible to get a job in the US with a European degree.

About me: I worked two years full time after my BSc and counting. I'm working full-time while stying the first year of my MSc in Finance which takes two years in total. The MiM degree is only one year and will take place simultaneously as my second year on the MSc in Finance. I'll switch to part time if my second year gets tough. I started out as a Financial Analyst and was promoted to Financial Associate at the SME I've worked at the past 2+ years.

Upon graduation, I'll have four years of post-graduate working experience, at least three of which is full-time.