  This work is devoted to the analysis of strong solutions to the
Abels-Garcke-Gr\"{u}n (AGG) model in three dimensions. First, we prove the
existence of local-in-time strong solutions originating from an initial datum
$(\mathbf{u}_0, \phi_0)\in \mathbf{H}^1_\sigma \times H^2(\Omega)$ such that
$\mu_0 \in H^1(\Omega)$ and $|\overline{\phi_0}|\leq 1$. For the subclass of
initial data that are strictly separated from the pure phases, the
corresponding strong solutions are locally unique. Finally, we show a stability
estimate between the solutions to the AGG model and the model H. These results
extend the analysis achieved by the author in {\it Calc. Var. (2021) 60:100} to
three dimensional bounded domains.
