In a recent report, sum-frequency excitation of a Raman-active phonon was experimentally demonstrated. This mechanism is the sibling of impulsive stimulated Raman scattering, in which the difference-frequency components of a light field excite a Raman-active mode. Here, we propose that also ionic Raman scattering analogously has a sum-frequency counterpart. We compare the four Raman mechanisms, photonic and ionic difference- and sum-frequency excitation, for three different example materials using a generalized oscillator model for which we calculate the parameters with density functional theory. Sum-frequency ionic Raman scattering completes the toolkit for controlling material properties by means of selective excitation of lattice vibrations.