  We study a multiple-spin exchange model on a triangular lattice, which is a
possible model for low-density solid 3He films. Due to strong competitions
between ferromagnetic three-spin exchange and antiferromagnetic four-spin one,
the ground states are highly degenerate in the classical limit. At least
2^{L/2}-fold degeneracy exists on the L*L triangular lattice except for the
SO(3) symmetry. In the magnetization process, we found a plateau at
m/m_{sat}=1/2, in which the ground state is "uuud state" (a collinear state
with four sublattices). The 1/2-plateau appears due to the strong four-spin
exchange interaction. This plateau survives against both quantum and thermal
fluctuations. Under a magnetic field which realizes the "uuud" ordered state, a
phase transition occurs at a finite temperature. We predict that low-density
solid 3He thin films may show the 1/2-plateau in the magnetization process.
Experimental observation of the plateau will verify strength of the four-spin
exchange. It is also discussed that this magnetization plateau can be
understood as an insulating-conducting transition in a particle picture.
