In terms of attire, one did not upstage the other by looking more sophisticated or fashionable—or elitist, God forbid.
So, Streep rewrote much of her dialogue, which led to tension with her co-star, Hoffman, who felt she was trying to upstage him.
Daily Pic (Venice Biennale Edition): Yuri Ancarani shows that medical magic can upstage the aesthetic kind.
1918 (adj.), 1921 (v.); the notion is of drawing attention to oneself (and away from a fellow actor) by moving upstage -- to the rear of the stage -- so that the other actor must face away from the audience. The noun upstage "back of the stage" is recorded from 1870.