  The ground state of the multiple-spin exchange model with up to the six-spin
exchange interactions on a triangular lattice in the magnetic field is
investigated within the mean-field approximation. By comparing the phase
diagrams of systems with and without the five- and six-spin interactions, we
find that the five- and six-spin interactions expand the ferromagnetic phase.
In contrast, the antiferromagnetic-like phases are contracted. A phase with a
1/2 plateau is also contracted by the five- and six-spin interactions. In
addition to the results that have not yet been reported for systems with up to
the four-spin interactions, we obtain new phases for systems with up to the
six-spin interactions. In particular, a 1/6 plateau appears in the low magnetic
field near the ferromagnetic phase in the magnetization process. This phase has
a twelve-sublattice structure in which a unit cell consists of seven spins
parallel to the magnetic field and five spins antiparallel to it.
