  We propose a modified Boltzmann nonlinear electric-transport framework which
differs from the nonlinear generalization of the linear Boltzmann formalism by
a contribution that has no counterpart in linear response. This contribution
follows from the interband-coherence effect of dc electric-fields during
scattering and is related to the interband Berry connection. As an application,
we demonstrate it in the second-order nonlinear Hall effect of the tilted
massive Dirac model. The intuitive Boltzmann constructions are confirmed by a
quantum kinetic theory, which shows that arbitrary $n$th-order nonlinear dc
response up to the first three leading contributions in the weak disorder
potential is handled by the same few gauge-invariant semiclassical ingredients.
