Should I do two internships at a time ? Please read.

Hi there, I'm in a bit of unique situation here. really needs some guidance. I just finished my third year. currently doing a 12 month internship at a large consumer&retail company doing M&A and strategy. previously worked in a boutique and a large bank (back office stuff). wasn't able to place a good IB/PE internship for this summer due to various reasons(lack of networking and school not being a target and etc). the current consumer&retail company is not really brand name but a pretty big company. I'm not even sure what the exit opps are from my current company.

I was given a part time internship opportunity during my current internship time which would open myself up for IB FT or next summer while working at my current job(this fund has a lot of ex-BB,MBB and etc. I'm pretty sure I can leverage their networks to get a better job next summer.) Reason I'm considering this is because I haven't succeeded on networking on my own , it never really resulted in a job offer or too many interviews. My school doesn't have too many alumni, I don't know if I try networking on my own again, the results would be any different. I thought 'networking" this way would be better ? They said I can work after regular hours and stuff. Working long hours is ok for me, I'm just concerned how my future employers will perceive this though. I feel like I might get a lot of questions on this. Please let me know what you think! thanks!