Methinks you can.
Linking Expressions from one Comp to the Master Comp (therefore only properties with Stop watches), then change the Master and it changes the Slaves.
Setup your Master Comp the way you want.
Dup it, then grab the tab of Master 2, pulling it up and away to make a second timeline.
Now if you use Effect>Text>Basic Text (Yeah, this might be the deal breaker because I don’t know if there’s a stopwatch for AE’s latest new Text Tool and I find it a bit of a pain to have to select the text I want to change the font /size,etc for then make changes in the Character Palette… maybe there’s an easier way, but you still need a stopwatch to link the expressions, so… that’s why I’m using the Effect>Text Effects).
Anyway Alt click the Fill Color on the Master 2, then pickwhip it to the Fill Color in the Master layer. Do the same for Size (font size in the Basic Text Effect), and any other property you want to ripple from the Master through the Slaves (Master 2, in this setup).
So now if you make the changes in the Master, it’s reflected in Master 2. Hey it even works without both comps being open (as I guess it should).
So dup the Dup as many times as you want for as many instances as you want. It might be a good idea to change the name of Master 2 to “Slave”, to limit confusion, then Dups of the Dup will be Slave2, Slave 3, etc.
And, if you want to change something in say Slave 47 to be different from the Master, just disable the expression and change away. Like I said you should be able to do this for anything that has a stopwatch, so transforms (animation – size, rotation,opacity…) and Shine is a go (if it’s in the Master).
It would take a little setting up, but worth the effort if I’m understanding what you want.