This mess is becoming really interesting.
Now we have multiple governments, which each regulate emissions, whom VW must satisfy when they bring these vehicles into compliance. Will VW use the same solution for all vehicles, or will the (presumably software) change vary by regulator?
Any fix will probably lower combustion temperatures and enrich the fuel/air mixture. This would not only lower fuel efficiency, but could also raise other emissions. If the exhaust system is carefully designed to the original requirements, that could require secondary changes to the vehicle too. Tightly-coupled systems and all that....
Here's a nice explanation of how Nitrogen oxides are created by exhaust. http://www.smogtips.com/failed-high-no-nitrous-oxide.cfm
More specifically, Nitrogen Dioxide (NO2) is what regulators are concerned about (at least the US EPA). That's generated at high combustion temperatures, but also with a lean fuel/air mixture (more Oxygen from the air, less Nitrogen from the fuel). https://www.dieselnet.com/tech/emi_gas.php