In our manuscript, we aim to investigate dark soliton behavior for the (2+1)-dimensional Davey–Stewartson-like equations with variable coefficients, which can be applied to the Bose-Einstein condensates or ultra-relativistic degenerate dense plasmas. Based on the dark one- and two-soliton solutions constructed, propagations and collisions of the solitons are illustrated, moreover, influences of the wave group dispersion P2(t) on the soliton structures are analyzed in detail, simultaneously. For P2(t) as the constant, stable propagations of the one solitons and elastic collisions between the two solitons are observed; For P2(t) as the linear function, velocities of the one solitons change during the propagations while the two solitons’ velocities alter during the collisions; With P2(t) being the trigonometric function, periodic characteristics for the one and two solitons emerge.