To encroach or prepare to take over (a thing, relationship, task or place that is or was somebody else's).
To come closer to, as if to catch or hunt.
To proffer (something) by force; to impose (something) on someone or into some area.
To impose (oneself) on others; to cut in.
To become apparent in an unwelcome way, to be forcibly imposed; to jut in, to intrude (on or into).