Double parton scattering (DPS) describes two colliding hadrons having interactions in the form of two hard processes, each initiated by a separate pair of partons. Just as for single parton scattering, the resummation of soft gluon exchange gives rise to a soft function, which is a necessary ingredient for obtaining rapidity evolution equations. For various regions of phase space, we derive the rapidity evolution and the scale evolution of double transverse momentum dependent parton distribution functions (DTMDs) as well as of the $p_{T}$-resummed cross section for double Drell-Yan like processes. This contributes to a framework that can be used for phenomenological DPS studies including resummation.