  We find closed formulas for the overlaps of Bethe eigenstates of
$\mathfrak{gl}(N)$ symmetric spin chains and integrable boundary states. We
derive the general overlap formulas for
$\mathfrak{gl}(M)\oplus\mathfrak{gl}(N-M)$ symmetric boundary states and give a
well-established conjecture for the $\mathfrak{sp}(N)$ symmetric case.
Combining these results with the previously derived $\mathfrak{so}(N)$
symmetric formula, now we have the overlap functions for all integrable
boundary states of the $\mathfrak{gl}(N)$ spin chains which are built from
two-site states. The calculations are independent from the representations of
the quantum space therefore our formulas can be applied for the $SO(6)$ and the
alternating $SU(4)$ spin chains which describe the scalar sectors of
$\mathcal{N}=4$ super Yang-Mills and ABJM theories which are important
application areas of our results.
