Context. Numerical studies have shown that the properties of the S0 galaxies with kinematics intermediate between fast and slow rotators are difficult to explain by a scenario of major mergers. Aims: We investigate whether the smoother perturbation induced by minor mergers can reproduce these systems. Methods: We analysed collisionless N-body simulations of intermediate and minor dry mergers onto S0s to determine the structural and kinematic evolution induced by the encounters. The original primary galaxies represent gas-poor fast-rotator S0b and S0c galaxies with high intrinsic ellipticities. The original bulges are intrinsically spherical and have low rotation. Different mass ratios, parent bulges, density ratios, and orbits were studied. Results: Minor mergers induce a lower decrease of the global rotational support (as provided by λe) 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 ɛe ~ 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 <ɛe < 0.7. In the experiments with S0b progenitor galaxies, minor mergers tend to spin up the bulge and to slightly decrease its intrinsic ellipticity, whereas in the cases of primary S0c galaxies they keep the rotational support of the bulge nearly constant and significantly decrease its intrinsic ellipticity. The remnant bulges remain nearly spherical (B/A ~ 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 (ɛe,intr), some of our models extend the linear trend found in previous major merger simulations towards higher ɛe,intr values, while others clearly depart from it (depending on the progenitor S0). 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. Conclusions: The smoother changes induced by minor mergers can explain the existence of S0s with intermediate kinematic properties between fast and slow rotators that are difficult to explain with major mergers. The different trends exhibited by ellipticals and S0 galaxies in the δ - ɛe diagram may be pointing to the different role played by major mergers in the build-up of each morphological type.