  Coupled dark matter-dark energy scenarios are modeled via a dimensionless
parameter $\xi$, which controls the strength of their interaction. While this
coupling is commonly assumed to be constant, there is no underlying physical
law or symmetry that forbids a time-dependent $\xi$ parameter. The most general
and complete interacting scenarios between the two dark sectors should
therefore allow for such a possibility, and it is the main purpose of this
study to constrain two possible and well-motivated coupled cosmologies by means
of the most recent and accurate early and late-time universe observations. We
find that CMB data alone prefers $\xi(z) >0$ and therefore a smaller amount of
dark matter, alleviating some crucial and well-known cosmological data
tensions. An objective assessment of the Bayesian evidence for the coupled
models explored here shows no particular preference for the presence of a
dynamical dark sector coupling.
