Here is what could happen with 96fm in this case. If they wanted to go all-in on KIIS, they could initiate a transition period of sorts before the eventual rebrand to said network name.
Here are some logos I assembled for what could be the perfect transition period for 96fm.
The first is the 96fm logo from 2015 when it first aligned with the KIIS Network, as that is one they would have to bring back from the dead, which means goodbye to the old 96fm logo. Then the colours could slowly change to the KIIS colours, before slapping the KIIS name on the 96fm logo and adapting a look similar to 97.3 FM Brisbane. Then a full-on rebrand to KIIS96.1 after that and then going all-in on Top 40/CHR like the East Coast metros.