  An open question of Sorin Popa asks whether or not every
$R^{\mathcal{U}}$-embeddable factor admits an embedding into $R^{\mathcal{U}}$
with factorial relative commutant. We show that there is a locally universal
McDuff II$_1$ factor $M$ such that every property (T) factor admits an
embedding into $M^{\mathcal{U}}$ with factorial relative commutant. We also
discuss how our strategy could be used to settle Popa's question for property
(T) factors if a certain open question in the model theory of operator algebras
has a positive solution.
