  We construct an off-shell extension of cubic interaction vertices between
massless bosonic Higher Spin fields on a flat background which can be obtained
from perturbative bosonic string theory. We demonstrate how to construct higher
quartic interaction vertices using a simple particular example. We examine
whether BCFW recursion relations for interacting Higher Spin theories are
applicable. We argue that for several interesting examples such relations
should exist, but consistency of the theories might require that we supplement
Higher Spin field theories with extended and possibly non-local objects.
