This paper is a follow-up contribution to our work (Sarkar in J Oper Theory, 73:433–441, 2015) where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of (Sarkar in J Oper Theory, 73:433–441, 2015) to the context of n-tuples of bounded linear operators on Hilbert spaces. Let $$T = (T_1, \ldots , T_n)$$ T = ( T 1 , … , T n ) be a pure commuting co-spherically contractive n-tuple of operators on a Hilbert space $${\mathcal {H}}$$ H and $${\mathcal {S}}$$ S be a non-trivial closed subspace of $${\mathcal {H}}$$ H . One of our main results states that: $${\mathcal {S}}$$ S is a joint T-invariant subspace if and only if there exists a partially isometric operator $$\Pi \in {\mathcal {B}}(H^2_n({\mathcal {E}}), {\mathcal {H}})$$ Π ∈ B ( H n 2 ( E ) , H ) such that $${\mathcal {S}}= \Pi H^2_n({\mathcal {E}})$$ S = Π H n 2 ( E ) , where $$H^2_n$$ H n 2 is the Drury–Arveson space and $${\mathcal {E}}$$ E is a coefficient Hilbert space and $$T_i \Pi = \Pi M_{z_i}$$ T i Π = Π M z i , $$i = 1, \ldots , n$$ i = 1 , … , n . In particular, it follows that a shift invariant subspace of a “nice” reproducing kernel Hilbert space over the unit ball in $${{\mathbb {C}}}^n$$ C n is the range of a “multiplier” with closed range. Our work addresses the case of joint shift invariant subspaces of the Hardy space and the weighted Bergman spaces over the unit ball in $${{\mathbb {C}}}^n$$ C n .