In this talk, we will present a study of quotients of multiplier algebras of certain complete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson space on the ball. We are particularly interested in the non-commutative Choquet boundaries for these quotients. Arveson's notion of hyperrigidity is shown to be detectable through the essential normality of some natural multiplication operators. We also highlight how the non-commutative Choquet boundaries of these quotients are connected with their Gelfand transforms being completely isometric. Finally, we isolate analytic and topological conditions on the so-called supports of the underlying ideals that clarify the nature of the non-commutative Choquet boundaries. This is joint work with Raphaël Clouâtre.