  We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field
theories (SCFTs) with both central charges identical: $a = c$. We construct
them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a
collection of $\mathcal{N}=2$ Argyres--Douglas theories of type
$\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In
this way, we construct infinitely-many theories that flow to interacting SCFTs
with $a = c$ in the infrared. Finally, we briefly highlight the features of the
SCFTs without $a = c$ that arise from generalizing this construction.
