The phrase "encroach on" means to intrude upon or trespass upon someone or something, typically in a gradual or persistent manner. Synonyms for this phrase include "invade," "trespass," "infringe," "penetrate," "intrude," "violate," "usurp," "impinge," "interlope," and "impair." These words all convey a sense of one party overstepping boundaries or restrictions set by another. Encroachment can happen in many different contexts, such as in personal relationships, property disputes, or legal matters. Using synonyms for "encroach on" can help to add variety and specificity to one's writing by providing a range of words that convey similar meanings.