  A large experimental program is being mounted to search for neutrinoless
double-beta decay over the next decade. Multiple experiments using different
target isotopes are being prepared to explore the whole parameter space allowed
for inverted-ordered light neutrinos, and have the potential to make
discoveries in several other scenarios, including normal-ordered light
neutrinos and other exotic mechanisms. We investigate to what extent long-range
and exotic short-range contributions may be distinguished by combining
measurements of the decay half-life across isotopes. We demonstrate how
measurements in two isotopes may facilitate a joint measurement up to a
two-fold degeneracy, and how a further measurement in a third isotope may
remove this degeneracy. We also highlight the precision of the nuclear matrix
elements needed to convert half-lives into information on the underlying decay
mechanism. Considering their correlations and uncertainties in the framework of
a global Bayesian analysis, we assess the consequences of a possible future
10-fold reduction in uncertainties. Our work motivates an experimental program
measuring neutrinoless double-beta decay in more than one isotope, as this
would break parameter degeneracies and advance our understanding of particle
physics beyond the Standard Model.
