With the first multi‐messenger observation of a binary neutron star merger (GW170817), new constraints became available for masses and radii of neutron stars. We introduce a class of hybrid EoS that fulfills all these constraints and predicts a region in the mass‐radius diagram that could be populated only by hybrid neutron stars with quark matter cores. A confirmation of this conjecture would be provided when the NICER radius measurement for the high‐mass pulsar PSR J0740 + 6620 yields a radius significantly less than 11 km. Would this radius measurement yield a result in excess of 12 km, this would allow for both, a purely hadronic and a hybrid nature of this star. In the latter case, the maximum mass could reach 2.6 M⊙ so that the lighter object in the asymmetric binary merger GW190814 could have been a hybrid star. We demonstrate that this high mass can be compatible with an early onset of deconfinement for stars with masses below 1 M⊙ and the occurrence of low‐mass twin stars. In such a case, the remnant of GW170817 could be a long‐lived hypermassive pulsar.