Again, as Spirit Manger said, start with this essay: http://www.peabody.jhu.edu/conservatory/admissions/tips/doubledegree.html
You can audition for a BM conservatory or music school program (free-standing, or part of a university or liberal arts college). For that, 1/4-1/3 of your classes would be liberal arts and 2/3-3/4 would be music, including theory and music history etc.
You can apply to a college or university BA program for music, which may or may not have a performance component (many don’t) and may or may not have auditions for admission (many don’t but you can submit an arts supplement with a recording, music resume, awards, concert programs, and music teacher letters of recommendation.) Some will have performance for credit, some will have only extracurricular performance.
You can apply to a college or university for any major at all, other than music, and continue with lessons, practice and extracurricular performance, and some will give credit or help pay for lessons. Lessons can be on or off campus of course.
You can try to double major, or major and minor. Music majors are usually intensive and sequential so it can be hard to combine with, say, a science, in a double major.
You can do a double degree, which is usually 5 years. If you had a strong interest in another area I would recommend that. Bard, Oberlin, Lawrence, Harvard/NEC, Tufts/NEC are often mentioned. But you can also attend Harvard or Tufts or any other school and do music off campus, privately, at NEC or elsewhere.
You can major in piano for a BM or music for a BA and do fine. You do not need to try to think of another area to study for backup. Music majors are respected by employers, grad schools and med/law school etc. If you do have another area of interest, that is another story.
Read the essay and see which student you feel you most resemble and come back anytime for more questions 