Can I submit more recommendation letters than what is specified on a college's website?

In order to apply to a summer program, I required a letter of recommendation from a teacher which I obtained from a Creative Writing teacher. After being accepted in the program, I read the letter and was absolutely astonished by how positively she viewed me despite a lack of strong connection. Throughout the school year, my bond with my other English teacher grew, and I became positive that I wanted her to write me a letter of recommendation for college. I asked her, and she gladly accepted. By that time my list of colleges was gaining substance, and I had found a few to which I definitively wanted to apply. Unfortunately, these colleges required or strongly suggested one letter of recommendation from a humanities teacher and one from a science teacher. I am torn between my two humanities teachers, one whose letter is absolutely astounding but with whom I have little connection, and one with whom I have very strong connection but whose letter would not likely surpass that of my other teacher. So: can I submit both, perhaps including one as supplementary material? Any advice given to help resolve this dilemma would be greatly appreciated. Thank-you. #college #teaching #college-major #recommendation #education #higher-education