We explore whether non-standard dark sector physics might be required to solve the existing cosmological tensions . The properties we consider in combination are : ( a ) an interaction between the dark matter and dark energy components , and ( b ) a dark energy equation of state w different from that of the canonical cosmological constant w = -1 . In principle , these two parameters are independent . In practice , to avoid early-time , superhorizon instabilities , their allowed parameter spaces are correlated . Moreover , a clear degeneracy exists between these two parameters in the case of Cosmic Microwave Background ( CMB ) data . We analyze three classes of extended interacting dark energy models in light of the 2019 Planck CMB results and Cepheid-calibrated local distance ladder H _ { 0 } measurements of Riess et al . ( R19 ) , as well as recent Baryon Acoustic Oscillation ( BAO ) and Type Ia Supernovae ( SNeIa ) distance data . We find that in quintessence coupled dark energy models , where w > -1 , the evidence for a non-zero coupling between the two dark sectors can surpass the 5 \sigma significance . Moreover , for both Planck+BAO or Planck+SNeIa , we found a preference for w > -1 at about three standard deviations . Quintessence models are , therefore , in excellent agreement with current data when an interaction is considered . On the other hand , in phantom coupled dark energy models , there is no such preference for a non-zero dark sector coupling . All the models we consider significantly raise the value of the Hubble constant easing the H _ { 0 } tension . In the interacting scenario , the disagreement between Planck+BAO and R19 is considerably reduced from 4.3 \sigma in the case of \Lambda CDM to about 2.5 \sigma . The addition of low-redshift BAO and SNeIa measurements leaves , therefore , some residual tension with R19 but at a level that could be justified by a statistical fluctuation . We conclude that non-minimal dark energy cosmologies , such as coupled quintessence or phantom models , may soften the existing cosmological tensions .