A cooling system is provided which includes, for instance, a coolant supply manifold, a multifunction coolant manifold structure, and multiple cooling structures. The multifunction coolant manifold structure includes a coolant-commoning manifold and an auxiliary coolant reservoir above and in fluid communication with the coolant-commoning manifold. The multiple cooling structures are coupled in parallel fluid communication between the coolant supply and coolant-commoning manifolds to receive coolant from the supply, and exhaust coolant to the coolant-commoning manifold. The coolant-commoning manifold is sized to slow therein a flow rate of coolant exhausting from the multiple cooling structures to allow gas within the exhausting coolant to escape the coolant within the coolant-commoning manifold. The escaping gas rises to the auxiliary coolant reservoir and is replaced within the coolant-commoning manifold by coolant from the auxiliary coolant reservoir.