An Advanced Maritime Emissions Control System (AMECS) includes several Exhaust Intake Bonnets (EIBs) of different size and/or shape, an Emissions Capture System (ECS), and an Advanced Maritime Emissions Control Unit (AMECU) mounted on an Unpowered Seagoing Barge (USB). The EIB includes a cage formed by downward curved ribs, a shroud which is lowerable to cover the ribs, a belt near a lower edge of the EIB for retaining and sealing the EIB to a stack, and a mechanism for tightening the lower edge of the EIB (and thus the belt) around the stack. The ECS lifts one of the several EIBs onto the stack of an Ocean Going Vessel (OGV). Exhaust from the stack is drawn through a large diameter duct to the AMECU. The AMECU processes the exhaust through multiple treatment stages. The stages include pre conditioning the exhaust, oxidizing, reducing, polishing, and precipitating.