Summer program advice

I’m applying to around six summer programs for this coming summer, but I’m not sure if that’s too much. The essays won’t be too much of a problem, but the teacher recommendations are what gets me. Should I ask one teacher for multiple letters or have different teachers write each of my recs? If I go with the first option, will those two or three teachers be annoyed since they’re already so busy? In class today, my math teacher told us about how someone wanted her to sponsor their science fair project and she didn’t know if she could because she was “too busy.” If I go with the second option, I’m not sure what I can do because I don’t know many of my teachers very well (there are only 3 or 4 that I know really well). What should I do? Thanks!

In my opinion, I would ask several different teachers for recs. For me it would seem too much to ask of one teacher, besides that teacher might not feel you are fully invested in a program and that you are summer program shopping. Also, you never really know who will give you that outstanding rec Best not to put all your eggs in one basket. Do any of your program dates conflict?