Is it appropriate to ask professors at which schools their recommendation letters have more power? Usually in United States, three letters of recommendation are required by graduate schools but some applicants might ask more than more than three professors (say five) for letters. In this situation, there might be an issue of choosing whose-letter-to-which-school. 

I wonder whether it is appropriate to ask each referee at which schools or departments they are relatively more well-known (having connections or interactions with professors in there) so that their letters are more powerful in there. 

If it is not appropriate to do so, are there any efficient ways for students to determine to which schools should they send a certain professor's letter?

I am a little awkward with my grammar in this question (including the title). Please feel free to edit my question if you are a native speaker of English. Thank you very much!
I would ask your references for "coaching help" with your letters and being strategic with who writes your letters to which schools. As part of the coaching, there are two questions I would ask:


"Do you (the letter writer) any connections to or experience with the programs I am applying to?". For example, did they attend a program? Do they collaborate with faculty in that program? Does your program regularly send students to a program? 
"What are you thoughts about the programs?" This allows you to make sure your reference is on good terms with the programs you are applying to. For example, if the graduate admission chair is feuding with you letter writer, this might be (unfairly) held against you.