Extra Internship (European MM PE) vs FT position

Hi there monkeys!

I have been a passive member of this community for some 3-ish years now. Thanks for all the interesting/funny content during this time. Time has come for me to post my first question.

I have to decide between joining a European MM PE (IK Partners - Gilde Buy-out - Waterland) for an internship in September 2022 and starting somewhere full-time. Since my profile is not strong enough to join a BB as an Analyst (the rejection e-mails keep coming in), I feel that I should take the opportunity and join the PE fund since it is unsure if I will ever get the chance to join later in my career and it would be beneficial for my network. I have not yet secured an offer for a FT and the PE asked me to confirm ASAP.

An important detail is that I will have spend 1 full year of doing internships before September 2022. I finished my Msc this summer (summa cum laude). Currently at a local PE, next a local M&A boutique and afterwards a more "prestigeous" boutique (HL - Lincoln - GCA Altium). So i am not sure if this extra internship is worth it.

Also, if I accept the internship I will have to start FT off-cycle (early Jan). 

What do you guys think? Shoot!