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We present the spectroscopic orbits of eleven nearby, mid-to-late M dwarf binary systems in a variety of configurations: two single-lined binaries (SB1s), seven double-lined binaries (SB2s), one double-lined triple (ST2), and one triple-lined triple (ST3). Eight of these orbits are the first published for these systems, while five are newly identified multiples. We obtained multi-epoch, high-resolution spectra with the TRES instrument on the 1.5m Tillinghast Reflector at the Fred Lawrence Whipple Observatory located on Mt. Hopkins in AZ. Using the TiO molecular bands at 7065 -- 7165 Angstroms, we calculated radial velocities for these systems, from which we derived their orbits. We find LHS 1817 to have in a 7-hour period a companion that is likely a white dwarf, due to the ellipsoidal modulation we see in our MEarth-North light curve data. We find G 123-45 and LTT 11586 to host companions with minimum masses of 41 M_Jup and 44 M_Jup with orbital periods of 35 and 15 days, respectively. We find 2MA 0930+0227 to have a rapidly rotating stellar companion in a 917-day orbital period. GJ 268, GJ 1029, LP 734-34, GJ 1182, G 258-17, and LTT 7077 are SB2s with stellar companions with orbital periods of 10, 96, 34, 154, 5, and 84 days; LP 655-43 is an ST3 with one companion in an 18-day orbital period and an outer component in a longer undetermined period. In addition, we present radial velocities for both components of L 870-44AB and for the outer components of LTT 11586 and LP 655-43.