  We extend the equivariant classification results of Escher and Searle for
closed, simply connected, non-negatively curved Riemannian $n$-manifolds
admitting isometric isotropy-maximal torus actions to the class of such
manifolds admitting isometric strictly almost isotropy-maximal torus actions.
In particular, we prove that such manifolds are equivariantly diffeomorphic to
the free, linear quotient by a torus of a product of spheres of dimensions
greater than or equal to three.
