When we talk about "encroaching upon" something, we often refer to a situation where one thing is gradually invading or taking over something else. There are several other words that can be used instead of "encroaching upon" such as intruding, impinging, infringing, trespassing, violating, and encumbering. These terms all imply a similar notion of overstepping boundaries or limitations. Whether it's a physical or metaphorical boundary, the connotation is the same, that one entity is imposing itself on another where it's not welcome. Synonyms are useful in making writing more dynamic, and in this case, they offer us a diverse range of choices to replace the repetition of "encroaching upon".