Can I do two summer internships with different dates?

Hi everyone, so I just received and accepted an offer from a firm I very much like. The internship is shorter than usual so I will have time left in my summer.

I just got an email inviting me to an interview from a firm I also like very much. It was my understanding that the second firm rejected me before, but recently I met with a very senior person at the firm and now they want to interview me. I don't know if those two events are related or I misunderstood my rejection the first time, but regardless I have the interview now.

The firms are in different cities. Although they are both asset managers, they operate in significantly different methods and their potential client base isn't the same. Is it acceptable for me to continue interviewing and potentially accepting a second internship even though I have one already?

Obviously if I had the two internships I would have to disclose it to both parties and decide on the dates of my internship so they don't allign. I don't think there would be anything legally stopping me from doing it if I received an offer from the second firm, but I wanted to learn if this would be a move that is frowned upon. I feel like doing this would convey to the firm that I may not be as commited to them in the long run, but as an international student it is hard to find internships and full time jobs, so I want to maximize my chances of receiving a full time offer. 

What are your thoughts on this?

TLDR; Can I do two summer internships if they have different dates?