Abstract: Coupled dark matter-dark energy scenarios arc 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 prefer 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.