c. 1600, "overstay, remain beyond the limit of;" 1680s, "stay longer than;" from out- + stay (v.). Related: Outstayed; outstaying.
overstay or outstay one's welcome
They outstayed their competitors
outsource
outspend
outspoken
outspread
outstanding
outstay
outstretch
outstrip
out-take
out-thrust
outvote