Résumé : Context. Determining ages of stars for reconstructing the history of the Milky Way remains one of the most difficult tasks in astrophysics. This involves knowing when it is possible to relate the stellar mass with its age and when it is not. The young a-rich (YAR) stars present such a case in which we are still not sure about their ages because they are relatively massive, implying young ages, but their abundances are a-enhanced, which implies old ages. Aims. We report the results from new observations from a long-Term radial-velocity-monitoring campaign complemented with high-resolution spectroscopy, as well as new astrometry and seismology of a sample of 41 red giants from the third version of APOKASC, which includes YAR stars. The aim is to better characterize the YAR stars in terms of binarity, mass, abundance trends, and kinematic properties. Methods. The radial velocities of HERMES, APOGEE, and Gaia were combined to determine the binary fraction among YAR stars. In combination with their mass estimate, evolutionary status, chemical composition, and kinematic properties, it allowed us to better constrain the nature of these objects. Results. We found that stars with M< M were all single, whereas stars with M> Mcould be either single or binary. This is in agreement with theoretical predictions of population synthesis models. Studying their [C/N], [C/Fe], and [N/Fe], trends with mass, it became clear that many YAR stars do not follow the APOKASC stars, favoring the scenario that most of them are the product of mass transfer. Our sample further includes two likely undermassive stars, that is to say of such as low mass that they cannot have reached the red clump within the age of the Universe, unless their low mass is the signature of mass loss in previous evolutionary phases. These stars do not show signatures of currently being binaries. Both YAR and undermassive stars might show some anomalous APOGEE abundances for the elements N, Na, P, K, and Cr; although, higher-resolution optical spectroscopy might be needed to confirm these findings. Conclusions. Considering the significant fraction of stars that are formed in pairs and the variety of ways that makes mass transfer possible, the diversity in properties in terms of binarity, and chemistry of the YAR and undermassive stars studied here implies that most of these objects are likely not young.