The combination of asteroseismologically-measured masses with abundances from detailed analyses of stellar atmospheres challenges our fundamental knowledge of stars and our ability to model them. Ancient red-giant stars in the Galactic thick disc are proving to be most troublesome in this regard. They are older than 5 Gyr, a lifetime corresponding to an initial stellar mass of about $1.2M\odot$. So why do the masses of a sizeable fraction of thick-disc stars exceed $1.3M\odot$, with some as massive as $2.3M\odot$ ? We answer this question by considering duplicity in the thick-disc stellar population using a binary population-nucleosynthesis model. We examine how mass transfer and merging affect the stellar mass distribution and surface abundances of carbon and nitrogen. We show that a few per cent of thick-disc stars can interact in binary star systems and become more massive than $1.3M\odot$. Of these stars, most are single because they are merged binaries. Some stars more massive than $1.3M\odot$ form in binaries by wind mass transfer. We compare our results to a sample of the APOKASC data set and find reasonable agreement except in the number of these thick-disc stars more massive than $1.3M\odot$. This problem is resolved by the use of a logarithmically-flat orbital-period distribution and a large binary fraction.