An engine system for a machine is disclosed. The engine system may have an intake manifold configured to direct air into a donor cylinder and a non-donor cylinder of an engine. The engine system may have a first exhaust manifold configured to direct exhaust from the non-donor cylinder to the atmosphere and a second exhaust manifold configured to receive exhaust from the donor cylinder. The engine system may further have a control valve configured to selectively direct a first amount of exhaust from the second exhaust manifold to the intake manifold and an after-treatment component configured to treat the first amount of exhaust. In addition, the engine system may have a controller configured to adjust a first operating parameter of the donor cylinder such that a ratio of an amount of a gaseous component and an amount of particulate matter in the first amount of exhaust exceeds a predetermined threshold.