I agree with many of the comments above. It really depends on your situation. If you really enjoy both the company and role of your internship and can see yourself staying there long term, then you should stay at the company. However, if you are unsure i would recommend trying different internships to see what you might like better.
Having multiple internships at a company solely depends on one’s career interest and their previous internship experience in that company(what they intend to learn through internship). Someone who has already worked on a project during the 1st internship will know if the work they were doing during that period will be beneficial for their career ahead. If the person feels that the work or project in which they were working is something they wanted to do or passionate about, then doing multiple internships will benefit in their career and gives them job satisfaction. And there is no urgent need for the person to explore different industries/companies.
I spent two summers with one company and one summer with another. The best part of staying with the same company for two years was that I was able to dive right in at the start of the second summer. It takes a long time to find your place in a company, so having the additional summer helped me a lot there.
Because I didn’t see myself working full time at this company, I also interned somewhere else. This helped me because I got to experience a completely different industry and a different kind of internship.
I think there are pros and cons to each, it’s all about what would be best for you.