Inappropriate to meet with bankers at other banks during SA program?

I recently accepted a summer internship offer at a BB in New York for summer 2020. I'm sending out some emails to thank people who did some informational interviews with me early in the process, including to people at other BBs that I didn't receive an internship at, just to thank them for their time and let them know where I ended up. Networking is all about building relationships, not just using people right, so I wanted to email these people, say thank you and suggest we meet up for coffee during my internship. I have no plans to leave the BB I'm interning at and move to another one after the internship, but I wonder if meeting people from other banks for coffee would send up some red flags, should my firm somehow find out, and if I should just stick to thanking them for their time.