Common App letter of Recommendation

Can one teacher send different recommendation letters to different colleges? For example, I will be applying to Rice and would like my teachers to make a Rice-specific letter, which they have told me they are willing to do. Is this possible through Common App? For the same teacher to send different letters of recommendation to different universities that tailor to each individual university?

I might be wrong about this but I THINK Common App is set up so that you invite a teacher to write a letter, they submit it to Common App and then you chose which colleges that letter goes to. I don’t think it’s possible for them to submit individual letters for specific colleges. I suppose if you only want a teacher to write a recommendation for 1 school (i.e. you want your Calc teacher to only write a rec for Rice) they could upload that and you could only use that rec for that 1 school. But you would want to be super careful not to accidentally send that letter anywhere else. And then that teacher couldn’t upload any other letters for you. I suppose one way to work around this would be to have your mail their letter rather than using Common App for your recommendations if the school is OK with that.