Measurements of $CP$ observables in $B0\to DK\ast 0$ decays are presented, where $D$ represents a superposition of $D0$ and $D¯0$ states. The $D$ meson is reconstructed in the two-body final states $K+\pi -$, $\pi +K-$, $K+K-$ and $\pi +\pi -$, and, for the first time, in the four-body final states $K+\pi -\pi +\pi -$, $\pi +K-\pi +\pi -$ and $\pi +\pi -\pi +\pi -$. The analysis uses a sample of neutral $B$ mesons produced in proton-proton collisions, corresponding to an integrated luminosity of 1.0, 2.0 and 1.8 $fb-1$ collected with the LHCb detector at centre-of-mass energies of $\sqrt{s} = $ 7, 8 and 13 TeV, respectively. First observations of the decays $B0\to D(\pi +K-)K\ast 0$ and $B0\to D(\pi +\pi -\pi +\pi -)K\ast 0$ are obtained. The measured observables are interpreted in terms of the $CP$-violating weak phase $\gamma$.