In 1977, Joan Plastiras gave a striking example of two non $*$-isomorphic C$^*$-algebras $\mathcal A$ and $\mathcal B$ such that $$\mathcal A \otimes M_2(\mathbb C) \simeq \mathcal B\otimes M_2(\mathbb C)$$ (http://www.ams.org/journals/proc/1977-066-02/S0002-9939-1977-0461158-9/S0002-9939-1977-0461158-9.pdf).

My question is this: can you find two non $*$-isomorphic C$^*$-algebras $\mathcal A,\mathcal B$ such that $$\mathcal A\otimes M_n(\mathbb C) \simeq \mathcal B\otimes M_n(\mathbb C), \ n=2,3?$$ Note that Plastiras' example does not satisfy this condition. Furthermore, can you find non $*$-isomorphic $\mathcal A, \mathcal B$ such that $$\mathcal A\otimes M_n(\mathbb C) \simeq \mathcal B\otimes M_n(\mathbb C), \ \forall n\geq 2$$ or does this condition imply that $\mathcal A\simeq \mathcal B$?