A system is disclosed for use with an engine. The system may have an intake manifold configured to direct air into combustion chambers of the engine. The system may also have an auxiliary device and an exhaust manifold configured to direct exhaust from the combustion chambers of the engine through the auxiliary device to the atmosphere. The system may additionally have a conduit associated with fewer than all of the combustion chambers of the engine and extending to the auxiliary device in parallel with the exhaust manifold, and an auxiliary valve disposed within the conduit and selectively movable between a flow-passing position and a flow-blocking position.