Recently, it has been found that classifying early-type galaxies into fast and slow rotators based on their kinematics is more in accordance with their physical properties than the traditional morphological classification of S0 and ellipticals. In the framework of the kinematic classification, observations by the ATLAS3D Project have found that approximately 10-20% of the lenticular galaxies (S0s) in their sample show hybrid properties between fast and slow rotators. Numerical studies of major to intermediate mergers or of several sequential minor mergers have successfully generated slow and fast rotator galaxies, but they barely populate the gap between these two types. Therefore, we explore whether mergers of higher mass ratios can generate these hybrid galaxies by studying collisionless N-body simulations of intermediate and minor dry mergers onto S0s and determining the structural and kinematic evolution induced by the encounters. We have found that intermediate to minor mergers are a feasible mechanism to generate galaxies with intermediate kinematic properties between fast and slow rotators. Additionally, we find that the elliptical galaxies follow the linear tendency in the plane of global anisotropy of velocities and intrinsic ellipticity envisioned by the major merger simulations whereas the S0s are more scattered in this plane. These trends give us clues about the role played by major mergers in the constitution of each morphological type. Our results suggest that major mergers may be responsible for the dynamical state of up to ~40-50% of the actual S0 galaxies.