1) a short piece forming a step in a ladder; a particular level in society, one's employment etc (rung)
2) (in a theatre) the raised structure on which the actors appear; a point, period or step in development; a journey, distance, between two stopping-places along a road or route (stage)
to settle a dispute (between two opposite sides, opinions etc) by acting as the chosen judge(s)
achieve settlement
to plead (with a person) to end a quarrel or to obtain a favour
mediate
to break in on another person's affairs without right or invitation
meddle, intervene
(of events, circumstances) to happen between others in time
mediate
to act to obtain agreement; to produce (something) as a result by doing this
try to bring to an agreement
to discuss in order to come to an agreement; to arrange (something) by discussion
bargain, discuss