  We formulate and close the boundary state bootstrap for factorizing
K-matrices in AdS/CFT. We found that there are no boundary degrees of freedom
in the boundary bound states, merely the boundary parameters are shifted. We
use this family of boundary bound states to describe the D3-D5 system for
higher dimensional matrix product states and provide their asymptotic overlap
formulas. In doing so we generalize the nesting for overlaps of matrix product
states and Bethe states.
