Yr Right and RatsoreA are probably closer to furious agreement than posts show.
Civil Aviation Safety Authority - Home
Conflict with other Modifications
The STC is normally approved based on a specific aircraft configuration. As additional modifications are installed, the interface and interaction with those unexpected modifications can be significant. The person installing the modification is required to review the STC and the aircraft being modified and ensure there are no unexpected modifications in the aircraft being modified that will conflict with the STC. The interaction with any such modifications must be evaluated. For complex interactions, specialist technical advice should be sought to ensure there are no adverse consequences. Installation of significant avionic equipment into an aircraft with a FADEC, is one example. Any change to the STC to ensure necessary compatibility must be separately approved.
My view if an existing STC exists Australian or foreign and you are installing with STC owners approval you have an already approved modification. All you need to do is ensure it is compatible with other mods to the aircraft. It then looks a bit grey as to whether a LAME can do that or whether a CAR35 is needed. What is clear is a unique mod is not required to cover where an STC exists. The approved STC may help resale too.