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"kind of porridge," 1670s, in the American colonies, variant of mash (n.) "soft mixture." Meaning "anything soft and thick" is attested from 1824.
command to sled dogs, first recorded 1862, as mouche, perhaps altered from French marchons! "advance!" (imperative of marcher "to march;" see march (v.)).
"to pound to a pulp," 1781, from mush (n.). Related: Mushed; mushing.
[perhaps an alteration of mash, ''something soft and pulpy'']
The face, esp the mouth and jaws: He pulled his mush away from the plate and sighed
[1859+; origin unknown; perhaps fr Romany, ''man'']