You negotiate when you have leverage. If you want leverage, you get another internship offer and ask for a higher rate; you walk if you do not get what you want

You negotiate when you have leverage. If you want leverage, you get another internship offer and ask for a higher rate; you walk if you do not get what you want. Realise that as an intern, your negotiating power is limited. Focus on what you can learn, and if it is a good company, whether you can turn your internship into a full-time position. Take these two factors into account and choose the company that is the best in this regard --- any increase in the hourly pay rate will pale in comparison to the upward arc you will put yourself on if you optimise for the two factors I have mentioned.