This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on Hilbert spaces. Let T = (T_1, \ldots, T_n) be a pure commuting co-spherically contractive n-tuple of operators on a Hilbert space \mathcal{ H} and \mathcal{ S} be a non-trivial closed subspace of \mathcal{ H}. One of our main results states that: \mathcal{ S} is a joint T-invariant subspace if and only if there exists a partially isometric operator \Pi \in \mathcal{ B}(H^2_n(\mathcal{ E}), \mathcal{ H})$ such that $\mathcal{ S} = \Pi H^2_n(\mathcal{ E})$, where H^2_n is the Drury-Arveson space and \mathcal{ E} is a coefficient Hilbert space and T_i \Pi = \Pi M_{ z_i}, i = 1, \ldots, n. In particular, our work addresses the case of joint shift invariant subspaces of the Hardy space and the weighted Bergman spaces over the unit ball in \mathbb{ C}^n.
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