I've spoken with a good number of students during this travel season who are prepared to send supplemental recommendation letters. I always tell students that we'll read whatever they send us, but that they need to keep the number of supplements reasonable. I fear that by not naming a specific number of recommendation letters, "reasonable" is being defined as the number each particular student has decided to send us. Let me see if I can explain where we stand on this.
UVa requires one recommendation letter as part of your application. Traditionally, your guidance/college counselor writes this letter. Now, many students feel as though there's a teacher who knows them better than their counselor, so they supplement the counselor letter with a recommendation from a teacher. This is often a good idea.
Some students don't stop at one supplemental teacher recommendation and we wind up getting several letters that basically say the same things. Teachers tend to know students in similar ways unless they moderate a club or activity in which the student is involved. The letters wind up being a tad redundant. The extras don't add anything to the application. In fact, if you have an admission officer who has been reading for eight hours before getting to your application, they might find plowing through your folder to be quite tedious.
If you feel strongly that you must send multiple recommendation letters, they should be from people who know you in different ways. Beyond that, they better know you and not your parents. Letters from people who are writing as a favor to your parents typically follow a formula: one paragraph about themselves, one paragraph about your lovely family and parents (as if we don't assume everyone comes from a lovely family with nice parents), and one paragraph, usually about two sentences long, that mentions some information gleaned from your resume and then asks that we give you our "full consideration" (wink, wink). Early in the season, these letters are kind of humorous (as if we weren't going to give you our full consideration before, but now that someone has asked us, we'll read everything and give you a shot). After a few months, though, you can imagine how they come across.
Bottom line: Quality over quantity is the best rule of thumb for all parts of the application, but especially for your recommendations. I'd rather read a nice, short letter from your counselor or a teacher that tells a story about you than get oodles of letters with sweeping generalizations that could apply to any smart, hardworking high school student.