  We compute the Hausdorff multifractal spectrum of two versions of multistable
L{\'e}vy motions. These processes extend classical L{\'e}vy motion by letting
the stability exponent $\alpha$ evolve in time. The spectra provide a
decomposition of [0, 1] into an uncountable disjoint union of sets with
Hausdorff dimension one. We also compute the increments-based large deviations
multifractal spectrum of the independent in-crements multistable L{\'e}vy
motion. This spectrum turns out to be concave and thus coincides with the
Legendre multifractal spectrum, but it is different from the Haus-dorff
multifractal spectrum. The independent increments multistable L{\'e}vy motion
thus provides an example where the strong multifractal formalism does not hold.
