  We generalize the relation between discontinuities of scattering amplitudes
and cut diagrams to cover sequential discontinuities (discontinuities of
discontinuities) in arbitrary momentum channels. The new relations are derived
using time-ordered perturbation theory, and hold at phase-space points where
all cut momentum channels are simultaneously accessible. As part of this
analysis, we explain how to compute sequential discontinuities as monodromies
and explore the use of the monodromy group in characterizing the analytic
properties of Feynman integrals. We carry out a number of cross-checks of our
new formulas in polylogarithmic examples, in some cases to all loop orders.
