Some subtypes (example: the asura and behemoth subtypes from Bestiary III) indicate that members of their subtype races have spell resistance equal to 11 + CR. My question is, does that SR increase as CR increases. So if say an asura started gaining levels in a character class and thus caused its CR to go up, would its spell resistance also go up? What if it increased CR through getting a template or advancing in racial hit dice?
Yes the SR will increase with every modification you apply on the monster. The formula 11 + CR is alwais valid