An engine system for a machine is disclosed. The engine system may have a first intake manifold configured to distribute air into a first cylinder bank of an engine. The engine system may also have a second intake manifold configured to distribute air into a second cylinder bank of the engine. The engine system may have a first exhaust manifold configured to discharge exhaust from the first cylinder bank to the atmosphere. The engine system may further have a second exhaust manifold configured to discharge exhaust from non-donor cylinders in the second cylinder bank to the atmosphere. In addition, the engine system may have a third exhaust manifold separate from the first and second exhaust manifolds and configured to recirculate exhaust from donor cylinders in the second cylinder bank to the first and second intake manifolds.