  We investigate the membership in double, triple or higher-order-multiplicity
systems of 54 pairs with at least one bright M dwarf in the solar
neighbourhood. These M dwarfs are potential targets of radial-velocity surveys
for exoplanets. We measure angular separations and position angles from optical
images taken with TCP and CAMELOT at the IAC80 telescope at the Observatorio
del Teide, and complement them with our measurements on photographic plate
digitizations. We also use data in the Washington Double Star Catalogue and
other bibliographic sources. We confirm the physical binding of 52 multiple
systems, for which we comprehensively compile, derive and provide basic
astrophysical parameters in a homogeneous way (spectral types, heliocentric
distances, projected physical separations, individual masses, estimated orbital
periods, binding energies). Of the 52 systems, 38 are double, 11 are triple and
three are quadruple with a variety of architectures. Four systems contain white
dwarfs, six systems display variations of position angle larger than 12 deg
(1/30 orbit) on a scale of decades and seven systems are located at less than
10 pc. We provide new information, or correct published data, of the most
remarkable multiple systems and identify some of them for high-resolution
imaging and spectroscopic follow-up.
