  We present a solvable ladder model which displays magnetization plateaus at
fractional values of the total magnetization. Plateau signatures are also shown
to exist along special lines. The model has isotropic Heisenberg interactions
with additional many-body terms. The phase diagram can be calculated exactly
for all values of the rung coupling and the magnetic field. We also derive the
anomalous behaviour of the susceptibility near the plateau boundaries. There is
good agreement with the phase diagram obtained recently for the pure Heisenberg
ladders by numerical and perturbative techniques.
