I cannot see it being able to be done. Theres just not enough wires. Basically whats missing is after you get your switched power to your light you need a path back to the main (source) neutral. Or any neutral really. You do have white wires in the 3 way switch boxed but they are acting as travellers and not neutrals. Sorry for your bum luck. I hate being short wires!
If you could pull a 3 wire to replace the 2 wire between the source power light fixture and the 3 way switch box on the right, than you could then feed a light fixture off that 3 way. I am not sure if thats easier for you...
So, the National Electric Code doesn't say anything about the number of outlets on a breaker, but it does specify the number of wires allowed in a junction box, which seems to be your main question.
Box size
Since you have no drywall, we can assume that you are using "New work" boxes, but you should check their labeled size (in cubic inches - ci) to be sure of what you're working with. A typical "deep", new-work box is 22ci. If you are using 12/2 Romex and putting an outlet in the box, the required size is:
- 6 conductors coming into the box: 6 * 2.25 = 13.5ci
- Your outlet counts as 2 conductors: 2 * 2.25 = 4.5ci
- The ground wires count as one: 1 * 2.25 = 2.25ci
- Required size: 20.25ci
So, you should be fine. If you're using 14/2 (probably - I went with the worst case for the example), the multiplier is 2ci rather than 2.25ci.
Wiring it together
If you have one pair coming in a box and one going out, using the screws of the outlet isn't a hack, and they even sell nice "backwire" outlets that are made for that. In the box where you are "splitting off" and you have three pairs, a pigtail to the outlet is probably better than filling all the holes in a backwire outlet. (Note, the pigtails don't count for the cubic inch calculations)
Also, in your "junction box" all the wires need to be folded nicely and pushed to the back before installing the outlet. The outlet shouldn't be used to force the wires into the box - you should be able to push the outlet all the way in with no resistance from the bundle in the back.
Best Answer
There are some splicing methods permitted inside walls, but ordinary wire nuts are not.
The usual solution is to use a junction box, with or without anything else in the box. For example, if your cable goes to a light fixture and you want to replace it with another light fixture a few feet away, connect the old & new cables with wire nuts inside the existing box, cover it with a blank plate, and run the new cable to a new box where you want it. The cover plate has to be accessible, but it can be painted or wallpapered to match your wall or ceiling, or hidden behind a picture. It just needs to be accessible without any special tools (except a screwdriver to remove the usual two screws holding it onto the box).