Can we specify eigen vectors and eigen values for MIMO pole placement

For MIMO system, there is a flexibility in eigen structure assignment, that is there can be more than one set of eigen vectors and eigen values that give feedback gain K right? In that case how actually matlab's Place command works for MIMO case?

K=place(A,B,P)  
[V1,D1]=eig(A-B*K)

Eventhough there can be different set of V1 associated with D1(poles) and K, Matlab place command followed by eig() always returns same V1.

Is there any way to specify the required D1 and P to get feedback gain K for MIMO case?

Thank you so much for your time.