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 1.2 M⊙. So why do the masses of a sizeable fraction of thick-disc stars exceed 1.3 M⊙, with some as massive as 2.3 M⊙? 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 1.3 M⊙. Of these stars, most are single because they are merged binaries. Some stars more massive than 1.3 M⊙ 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 1.3 M⊙. This problem is resolved by the use of a logarithmically flat orbital-period distribution and a large binary fraction.