Adding Second Light to 3 Way Switch and Light

You can not add a new fixture at switch "C" in the diagram. There is no neutral.
The only place you can add a light in the diagrams is "strategically placed junction box" or any existing light fixture.

This switch is located in a box with switch for another lighting circuit that does have a neutral. Can I connect to the neutral of the other switch and still run the main feed from the main switch and have it work correctly?

I think you need to describe or diagram what you actually have, rather than possibly miss-leading us with a diagram that is not similar. That one was based on a 4way switch setup to power a bunch of lights on either side of the beam, while minimizing beam crossings.

Since I doubt that you have either the 4way or the junction box, where is the load location(cable to lights) ? Is it at same 3way where the power comes in, or at the second 3way?

Right now, all we can say is connect your new light at one of the existing lights.

ant123 said:

This switch is located in a box with switch for another lighting circuit that does have a neutral. Can I connect to the neutral of the other switch and still run the main feed from the main switch and have it work correctly?

Click to expand...

Only if the neutral is from the same circuit. You can not cross neutrals between circuits.