  Geodesic trapping is an obstruction to dispersive estimates for solutions to
the Schr\"odinger equation. Surprisingly little is known about solutions to the
Schr\"odinger equation on manifolds with degenerate trapping, since the
conditions for degenerate trapping are not stable under perturbations. In this
paper we extend some of the results of [CM14] on inflection-transmission type
trapping on warped product manifolds to the case of multi-warped products. The
main result is that the trapping on one cross section does not interact with
the trapping on other cross sections provided the manifold has only one
infinite end and only inflection-transmission type trapping.
