We analysed collisionless N-body simulations of intermediate and minor dry mergers onto S0s to test whether these mergers can generate S0 galaxies with kinematics intermediate between fast and slow rotators. We find that minor mergers induce a lower decrease of the global rotational support than encounters of lower mass ratios, which results in S0s with properties intermediate between fast and slow rotators. The resulting remnants are intrinsically more triaxial, less flattened, and span the whole range of apparent ellipticities up to $ε_\mathrm{e} \sim 0.8$. They do not show lower apparent ellipticities in random projections than initially; on the contrary, the formation of oval distortions and the disc thickening increase the percentage of projections at $0.4 < ε_\mathrm{e} < 0.7$. In the experiments with S0b progenitor galaxies, minor mergers tend to spin up the bulge and to decrease slightly its intrinsic ellipticity, whereas in the cases of primary S0c galaxies they keep the rotational support of the bulge nearly constant and decrease significantly its intrinsic ellipticity. The remnant bulges remain nearly spherical ($B/A \sim C/A > 0.9$), but exhibit a wide range of triaxialities ($0.20 < T < 1.00$). In the plane of global anisotropy of velocities ($δ$) vs. intrinsic ellipticity ($ε_\mathrm{e,intr}$), some of our models extend the linear trend found in previous major merger simulations towards higher $ε_\mathrm{e,intr}$ values, while others depart from it. This is consistent with the wide dispersion exhibited by real S0s in this diagram compared with ellipticals, which follow the linear trend drawn by major merger simulations. The different trends exhibited by ellipticals and S0 galaxies in the $δ$ - $ε_\mathrm{e}$ diagram may be pointing to the different role played by major mergers in the build-up of each morphological type.

Corrected typos. 20 pages, 14 figures. Accepted for publishing in A&A