  A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was
recently identified in arXiv:1702.01482. We identify here in a similar way a
family of A_{2n-1}^(2) integrable open spin chains with U_q(D_n) symmetry, and
two families of D_{n+1}^(2) integrable open spin chains with U_q(B_n) symmetry.
We discuss the consequences of these symmetries for the degeneracies and
multiplicities of the spectrum. We propose Bethe ansatz solutions for two of
these models, whose completeness we check numerically for small values of n and
chain length N. We find formulas for the Dynkin labels in terms of the numbers
of Bethe roots of each type, which are useful for determining the corresponding
degeneracies. In an appendix, we briefly consider D_{n+1}^(2) chains with other
integrable boundary conditions, which do not have quantum group symmetry.
