There are many synonyms for the phrase "intrude on." Some of them include "encroach upon," "violate," "trespass," "invade," "intrude upon," "impinge," "interlope," "butt in," and "meddle with." Each of these words carries a slightly different connotation, but all convey the idea of someone or something crossing a boundary they shouldn't. Whether it's someone invading your privacy or an unwanted thought that keeps intruding on your mind, these synonyms offer a variety of ways to express the concept of intrusion. So the next time someone is invading your space, you can tell them to stop encroaching upon your boundaries!