Hyperreflexivity of von Neumann algebras and similarity of finitely generated C^*-algebras

Let A be a C^*-algebra. We say that A satisfies the SP if every bounded homomorphism A→ B(K), with K a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive algebras by projections. We prove that our third hypothesis is equivalent to every finitely generated C*-algebra satisfying the SP. We show that to prove that every von Neumann algebra is hyperreflexive it is enough to show that when one extends a hyperreflexive algebra by a single projection it remains hyperreflexive.