Extending power from existing three-way switch circuit
Let's go to the store and get some colored tape, so we don't lose our minds.  We don't need to distinguish two travelers from each other, so a pair of travelers can be the same color.  We do however have two sets of travelers in close proximity, and two switched-hot colors which I'm making red and purple. 

So now in color: 



In order to feed an additional switch+lamp combo, you need always-hot and neutral.  Do you see it in the right hand switch box? Yes, you do, but how? 

Well, you've got always-hot in one cable and neutral in the other cable -- Oh wait. 

You can't do that

You can't pull power off one cable and return it on another cable.  Currents must be equal in each cable.  The answer is "NO". 

It would be yes if they were all wires in one conduit.  Using cable between the switch groups sinks you.