  The tension among inferences of Hubble constant ($H_0$) is found in a large
array of datasets combinations. Modification to the late expansion history is
the most direct solution to this discrepancy. In this work, we examine the
viability of restoring the cosmological concordance with a novel version of
transitional dark energy (TDE). The main anchors for the cosmic distance scale:
cosmic microwave background (CMB) radiation, baryon acoustic oscillation (BAO),
and Type Ia supernova (SNe Ia) calibrated by Cepheids form a "impossible
trinity", i.e., it's plausible to reconcile with any two of the three but
unlikely to accommodate them all. Particularly, the tension between BAO and the
calibrated SNe Ia can not be reconciled within the scenarios of late dark
energy. Nevertheless, our analysis suggests that the TDE model can reconcile
with CMB and SNe Ia calibrated by its absolute magnitude ($M_{\rm{B}}$) when
the equation of state (EoS) of DE transits around $z\sim1$. Meanwhile, we see a
positive sign that the EoS transits with the inclusion of a local prior on
$M_{\rm{B}}$, whereas the opposite is true without the $M_{\rm{B}}$ prior.
