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I have two overhead lights controlled by two separate circuits of two three-way switches.
One is wired like this:
The other is wired like this:
There are two three-way switches for the overhead light in a three gang box. Is there a way to add a separately controlled single pole switched light using the feed from the three-way switches just before the overhead light in the first diagram.
If both switches are of the type 2 configuration in your diagrams, then no. You need unswitched power from somewhere to either the new light or new switch. For example, if either of the switches in the 3 gang box were of the type 1 configuration, then you have unswitched power and can add another switch.
To do what you want you would need to run another conductor from where there is unswitched power available.
What you call circuit power supply cable, electricians call the feed. A feed is a hot and its neutral uninterrupted by any device from the source (the panel). You need access to the feed to tap into that circuit. In both of your diagrams the feed is in the box with switch #1. In your 1st diagram switch #2 has the neutral but not its un-switched hot in the 2nd diagram switch #2 doesn't have either an un-switched hot or its neutral.
Here is an utterly stupid solution to the problem (please don't). If you got a double pole switch (not a three-way - not a four-way) and you were willing to install two fixtures to be controlled by this switch, you could run two conductors (one to each light) and one of the two lights will be on when the switch is on, and neither will be on when the switch is off.
This is for academic purposes only. I do not recommend doing this unless you really want to confuse someone.
