Have 2 Part-Time Internship Opportunities - Can I take both?

I'll be working for a FINRA certified firm but I don't believe I'll be a FINRA registered employee. When I applied in the Summer, we had to declare any outside business activities I believe, but they renewed my contract and haven't asked for any updates nor provided any guidance since I am a part-time intern right now. I recently was offered an opportunity as a part-time analyst for a hedge-fund and the hedge fund knows I currently work at the FINRA certified firm but the FINRA regulated firm does not know anything about the offer from the hedge fund. Should I ask my current supervisor if I can take the position, or just take it since there is a low chance my current internship figures out.

I would be a part-time intern for both companies and it would be in the same industry. What is the worst that can happen here? FINRA regulated firm figures out I have undeclared outside business activities and they withdraw the at-will employment full time offer that I accepted for Fall 2022? If that's the worst case and firm 2 still likes me and allows me to work I assume they could just extend an offer. Either firm would be great to work for on my end of things and the experience I'd be getting at the hedge fund would be incredibly valuable in terms of being a quantitative research intern part-time.