  We explore the relation between the nuclear matrix elements of neutrinoless
double-beta ($0\nu\beta\beta$) decay and two other processes: double
Gamow-Teller (DGT) and double-magnetic dipole (M1M1) transitions, with focus on
medium-mass to heavy nuclei studied with the proton-neutron quasiparticle
random-phase approximation (pnQRPA) framework. We explore a wide span of
isoscalar proton-neutron pairing strengths covering the typical range of values
that describe well $\beta$- and two-neutrino $\beta\beta$-decay data. Our
results indicate good linear correlations between $0\nu\beta\beta$ and both DGT
and M1M1 matrix elements. Together with future measurements of DGT and M1M1
transitions, these correlations could help constrain the values of the
$0\nu\beta\beta$-decay nuclear matrix elements.
