MFE after B.Sc. in BA and Economics

Hey everyone,

I‘m currently pursuing my bachelor in BA and Economics at a semi-target in Germany. During my bachelor I find my self more interested in the quantitative part of my study. I was in general very interested in physics and engineering beside of finance during my time in school, but choose BA in order to chase the dream of breaking into IB/PE. 
Now I feel like IB could make me unhappy in long term, because of the low intellectual requirements and data sience or financial engineering, would make me qualified for both (Quant-F and IB/PE). 
I already interned in a M&A boutique and will join a MM in Spring Break and I like it very much, but don’t want to close the door to quant Finance. 

Therefore I can think of two ways:
1) Doing an bachelor of engineering or physics after my current bachelor and than do a Master in quant Finance or something related like MFE (3 Years more of study)
Or
2) Doing an MFE with the degree I am currently pursuing. I don’t know whether this is possible or not, therefore I am asking for advice and a estimation on how likely it is for me to get in a Top MFE Programm (EU)

Thanks a lot for any answers!