Should I do MBA, MBA/JD or neither? (Non traditional career path so far) please help!

I’m mostly just interested in Harvard/Stanford/UPenn.

Background: UK undergrad 3yr(top 5 not Oxford/Cambridge) then MFE 2yr, for the past year and a half in one of the top PE as analyst in portfolio construction. Just got promoted to associate. I’m thinking if I should do MBA maybe after another 2-3 years.

Cons — forgoing 2 years of career progression; and pay (by then probably would be missing out for at least 350k a year). I’m slightly concerned about career progression especially since I already spent 2 years on MFE. Pros — more connected, since I don’t have much school connections in US. A more traditional stamp of approval. Might be useful when my career progresses.

Also on JD/MBA — I always wanted to learn more about law, and unlike MBA this would actually be a learning opportunity, versus in MBA I doubt I can learn a lot from it. Also would be helpful as my career progresses and if I want to pivot to other sector, if want to start my own shop one day or maybe even politics lol. But obviously this would be even more time consuming, 3-4 years of opportunity cost. Also I have no real intention (at least rn) of becoming a lawyer.