  Motivated by the increasing number of systems featuring multiple bands at low
energy, we address the Boltzmann approach to transport in a multiband weakly
disordered noninteracting crystal subject to a small electric field. In
general, the multiband structure leads to a considerable complication of the
Boltzmann equation. Indeed, even in the presence of elastic impurity
scattering, one needs to compute for each band and momentum the dressed
velocities, which account for scattering events. Here we provide a
semianalytical solution to the Boltzmann equation that reduces such a
challenging numerical task to the much simpler numerical computation of a small
tensor whose dimension is set by the number of bands at the Fermi level. This
approach further allows us to discuss the interplay of symmetry and disorder
for different impurity types, including those originating from random-matrix
Wigner ensembles. As an example of application, we consider the 2D isotropic
Rashba metal and we discuss, in a full analytical fashion, how different types
of disorders may break the exactness of the relaxation-time approximation and
induce transport anisotropy, and may allow one to identify the presence of
spin-orbit coupling as deviations of the conductivity from the Drude behavior.
