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M-dwarfs in extremely wide binary systems are very rare, and may thus havedifferent formation processes from those found as single stars or closebinaries in the field. In this paper we search for close companions to a newsample of 36 extremely wide M-dwarf binaries, covering a spectral type range ofM1 to M5 and a separation range of 600 - 6500 AU. We discover 10 new triplesystems and one new quadruple system. We carefully account for selectioneffects including proper motion, magnitude limits, the detection of closebinaries in the SDSS, and other sample biases. The bias-corrected totalhigh-order-multiple fraction is 45% (+18%/-16%) and the bias-correctedincidence of quadruple systems is < 5%, both statistically compatible with thatfound for the more common close M-dwarf multiple systems. Almost all thedetected companions have similar masses to their primaries, although two verylow mass companions, including a candidate brown dwarf, are found at relativelylarge separations. We find that the close-binary separation distribution isstrongly peaked towards < 30AU separations. There is marginally significantevidence for a change in high-order M-dwarf multiplicity with binding energyand total mass. We also find 2-sigma evidence of an unexpected increasedhigh-order-multiple fraction for the widest targets in our survey, with ahigh-order-multiple fraction of 21% (+17%/-7%) for systems with separations upto 2000AU, compared to 77% (+9%/-22%) for systems with separations > 4000AU.These results suggest that the very widest M-dwarf binary systems need highermasses to form or to survive.

The High-Order-Multiplicity of Unusually Wide M-dwarf Binaries: Eleven New Triple and Quadruple Systems