The combined effects of rotation and mass accretion on the evolution of binary systems are investigated in this work. Rotational binaries provide us with a promising channel that could explain the abnormal phenomenon of the nitrogen abundances in Groups 1 and 2 of the Galactic Hunter diagram. Group 1 contains fast-rotating but nitrogen-unenriched stars, whereas Group 2 includes apparently slowly rotating but nitrogen-enhanced stars. The donor star suffers from heavy mass loss that progressively exposes deep layers of nitrogen and corresponding angular momentum loss that can efficiently spin the star down. Rapid-rotation stars without nitrogen enrichment may be related to mass gainers that had accreted little matter from a close companion and then been spun up to rapid rotation. Nitrogen enrichment of mass gainers can be greatly suppressed by low accreting efficiency, which is induced by critical rotation, thermohaline mixing, and the gradient of mean molecular weight. Nitrogen enrichment due to mass accretion appears to be more efficient than that due to rotational mixing, because there exist thermohaline instabilities during Roche lobe overflow. The mixing in the enlarged convective core reduces carbon and nitrogen abundances but increases oxygen abundances in mass gainers. This process significantly triggers CNO cycling but does not support CN cycling. The orbital separation can be widened because of the nonconservative mass transfer, and this process gives rise to weak tidal torques. Therefore, invoking binaries has the potential to simultaneously explain the observed stars in Groups 1 and 2 of the Galactic Hunter diagram.