To insert something (or oneself) between other things.
To interrupt a conversation by introducing a different subject or making a comment.
To intervene in a dispute, or in a conversation.
To be inserted between parts or things; to come between.
To offer (one's help or services).
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).