Context: The physical interpretation of scattering line polarization offers a novel diagnostic window for exploring the thermal and magnetic structure of the quiet regions of the solar atmosphere. Aims: We evaluate the impact of isotropic collisions with neutral hydrogen atoms on the scattering polarization signals of the 13 lines of multiplet 42 of Ti i and on those of the K line and of the IR triplet of Ca ii, with emphasis on the collisional transfer rates between nearby J-levels. Methods: We calculate the linear polarization produced by scattering processes in a plane-parallel layer illuminated by the radiation field from the underlying solar photosphere. We consider realistic multilevel models and solve the statistical equilibrium equations for the multipolar components of the atomic density matrix. Results: We give suitable formulae for calculating the collisional rates as a function of temperature and hydrogen number density. We confirm that the lower levels of the 13 lines of multiplet 42 of Ti i are completely depolarized by elastic collisions. Upper-level depolarization caused by the collisional transfer rates between nearby J-levels turns out to have an unnoticeable impact on the emergent linear polarization amplitudes, except for the λ4536 and λ4544.7 lines. Concerning the Ca ii lines, we show that the collisional rates play no role in the polarization of the upper level of the K line, while they have a rather small depolarizing effect on the atomic polarization of the metastable lower levels of the Ca ii IR triplet. Conclusions: Although the collisional transfer rates seem to play a minor role for most of the lines we considered in this paper, except, for example, for the magnetically insensitive λ4536 line of Ti i, they might be important for other atomic or molecular systems with closer J-levels (e.g., hyperfine structured multiplets and/or molecules). Therefore, future research in this direction will be worthwhile. Appendices A and B are only available in electronic form at http://www.aanda.org