The phrase "encroaching up on" refers to the act of gradually invading or intruding upon something or someone's space or territory. Some synonyms for this phrase include infringing, encumbering, impinging, invading, crowding, and usurping. Other synonyms that have a similar meaning include trespassing, creeping, encroaching, advancing, and overstepping. The use of such words helps to emphasize the idea of unwanted and unwarranted intrusion. In any case, using these synonyms can help to create a more descriptive and engaging language while expressing the concept of "encroaching up on" in a more impactful way.