Context. Carbon abundances in first-ascent giant stars are usually lower than those of their main-sequence counterparts. At moderate metallicities, stellar evolution of single stars cannot account for the existence of red-giant branch stars with enhanced carbon abundances. The phenomenon is usually interpreted as resulting from past mass transfer from an evolved binary companion now in the white dwarf evolutionary stage. Aims. We aim to confirm the links between [C/O] enhancement, s-process element enhancement and binary fraction using large-scale catalogues of stellar abundances and probable binary stars. Methods. We use a large data set from the 17th data release of the SDSS-IV/APOGEE 2 survey to identify carbon-enhanced stars in the Galactic disk. We identify a continuum of carbon enrichment throughout three different sub-populations of disk stars and explore links between the degree of carbon enrichment and binary frequency, metallicity and chemical compositions. Results. We verify a clear correlation between binary frequency and enhancement in the abundances of both carbon and cerium, lending support to the scenario whereby carbon-enhanced stars are the result of mass transfer by an evolved binary companion. In addition, we identify clustering in the carbon abundances of high-α disk stars, suggesting that those on the high metallicity end are likely younger, in agreement with theoretical predictions for the presence of a starburst population following the gas-rich merger of the Gaia-Enceladus/Sausage system.