Switch – Adding Light to Existing 3-Way Switch Configuration

The proposed wiring shown as Revision 1 in the original drawings is not code compliant. Under NEC 300.3(B), all wires for a given circuit must be in the same cable or raceway. In your example, the new lights get the hot lead from a single wire from the switch and the neutral from a separate cable or raceway from the old fixture.

Basically you need a balanced load in each cable or raceway (hot out/neutral back or hot out/switched hot back) to prevent the possibility of induction heating.

As @Speedy Petey suggests, a much simpler, and code compliant method, is to run a cable with a neutral and a switched hot from the existing fixture to the new fixtures.

UPDATE: Based on the added drawing in Revision 2, the proposed circuit is now code compliant. Also, as @Ben noted, any white wire used as a hot that is exposed in a box or fixture must be marked black or red with tape, paint or marker to show that it is hot.

You can get pretty close.

"...looks like a wall switch but without wires behind..." Assuming here that your looking for the standard TOGGLE light switch, then you're not likely going to find the exact product.

If Decora or paddle style wall switch is acceptable, then replace both existing 3 way ends with this or this (the difference is the first is on/off only, the second also Dims- choose the dimmer if the hall light is dimming compatible).

For the middle location choose this wireless switch plus a mounting bracket and any standard Decora or paddle switch wall plate.

Initial set-up (specifically linking) is slightly confusing if you've never before used Insteon products, wiring is however straight-forward. Insteon (also known as smarthome.com) does have good phone support (although their phone system produces horrible call quality-if that happens ask the support person to call you back as calls in that direction don't seem to be affected).

You also need a standard USB cable and perhaps an adapter to charge the wireless switch. (the middle switch will only need charging a few times a year). Honestly you likely already have this standard USB cable, it's pretty standard and the same used to connect most camera's and non-apple phones to a computer or charger. (I put smarthome.com links for the last two because those two items appear to cost much more when purchased via amazon.)

Disclaimer: I do NOT work for Insteon/Smarthome.com. I do work for a company that has a sales/installation agreement with Instean/Smarthome.