  We establish Ohno-type identities for multiple harmonic ($q$-)sums which
generalize Hoffman's identity and Bradley's identity. Our result leads to a new
proof of the Ohno-type relation for $\mathcal{A}$-finite multiple zeta values
recently proved by Hirose, Imatomi, Murahara and Saito. As a further
application, we give certain sum formulas for $\mathcal{A}_2$- or
$\mathcal{A}_3$-finite multiple zeta values.
