I was able to pass a wire (after much digging around for a route) from my new receptacle to another receptacle that has both sets of terminals filled, so it is a "middle of the run".
I added the new receptacle's three wires to that, and it is working showing two yellows on my three-light tester, as it should.
So I avoided the wire nut "issue", but I am still not clear on the series vs parallel thing since it seems to me, I have stolen from the next in the run by tapping in like that.
Does it make any difference if you tap in sideways like I did from adding another receptacle to the "run", for what you can draw from the receptacle?
Thanks.