  Let $D$ be a homogeneous bounded domain of $\mathbb{C}^n$ and $\mathcal{A}$ a
set of (anti--Wick) symbols that defines a commutative algebra of Toeplitz
operators on every weighted Bergman space of $D$. We prove that if
$\mathcal{A}$ is rich enough, then it has an underlying geometric structure
given by a Lagrangian foliation.
