The AJ6 and the evolved AJ16 were Jaguar's replacement for the venerable XJ6. They can be found in the six cylinder XJS, XJ40, X300, and in the early model Aston Martin DB7. From '95-'97 the XJR featured a blown unit with an Eaton M90 Super Charger. Displacement ranged from 3.2 and 4.0.
Here is what I've heard concerning performance improvements on these engines. I haven't done any of this myself yet, but a lot of it is just common sense.
I don't own a blown engine, so I'll cover NA models.
If you are in the US you can gain some improvements by switching to Euro spec cams.
After that: blueprint and balance, then port the engine.
20-40hp can reportedly be gained by installing better flowing mufflers and cats, along with the removal of the two upstream mufflers.
I haven't heard anything positive concerning Bywater parts, but I have no experience with them so I'll just suggest caution and research.