  The 4-dimensional effective theory arising from an induced gravity action for
a co-dimension greater than one brane consists of multiple galileon fields
pi^I, I=1...N, invariant under separate Galilean transformations for each
scalar, and under an internal SO(N) symmetry. We study the viability of such
models by examining spherically symmetric solutions. We find that for general,
non-derivative couplings to matter invariant under the internal symmetry, such
solutions exist and exhibit a Vainshtein screening effect. By studying
perturbations about such solutions, we find both an inevitable gradient
instability and fluctuations propagating at superluminal speeds. These findings
suggest that more general, derivative couplings to matter are required for the
viability of SO(N) galileon theories.
