I think it's a great idea. Water has been used quite a bit in an effort to reduce NOx emissions since they are cause by the high heat of combustion when excess O2 is around, which is exactly what diesel engines do.
https://www.dieselnet.com/tech/engine_water.php
If the second pump were to inject a small quantity of water some short time after combustion has started it would absorb a great deal of heat that would have created NOx or been absorbed by the cooling system to turn to into steam, which expands some 1700 times its original size. This gives power and reduces NOx at the same time.
with enough water it is basically it is an internal combustion steam engine. Of course the complexity of adding another injection pump and injector and getting everything timed correctly would be non-trivial. Small amounts of oil can be added to the water to lubricate the water IP, that how steam engines did it.
http://www.econologie.info/share/partager/1251395965azE1K3.pdf