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I have 2x 3-gang boxes, each with 3x 3-way switches in each box. All are on the same 15A breaker.

I have wired them together and I'm just connecting the switches now. I have:

 -------- ---------
BREAKER --14/2-- |3x-3WAY| --3x14/3-- |3x 3-WAY| ---3x14/2-- LIGHTS
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The 3-gang boxes are connected with 3 runs of 14/3 cable.

My question is: should I splice the neutrals together (and the grounds) at the second 3-gang box (load side)? It seems like it doesn't matter, since they could just as well be going to 3x 1-gang boxes on the load side in which case they would NOT be connected.

To clarify - I'm not asking if I should connect neutral to ground (I know I shouldn't do that). I'm asking if I should connect all the neutrals together and pigtail off that or just treat each switch independently on the load side.

Is there a standard way to do it?

If you have an electrical box at the second switch bank location with enough cubic inch volume you should really keep each circuit separate (i.e. not inter tie the neutrals). The primary reason is that you want the current in the hot line (in this case the travellers) and the neutral of each cable to be the same.

Another good reason for that would be that at some time in the future it may be desirable to bring an alternate power feed to the first switch bank location to feed one lighting circuit separately. You do not want to intermix the neutrals from two separate circuits.

Neutral is not ground

Neutral is the normal path of current return. Ground is an emergency path, only used if something is seriously wrong (in lieu of sending power through a human, and it helps to get breaker to trip). Because of that, it's OK to spiderweb all grounds to each other. This should never be done with neutral.

Currents must be equal in each cable or conduit

Because AC current in wires causes AC magnetism, and the wires' magnetism must cancel each other out. If it doesn't, it will cause eddy current heating, and noise/vibration leading to fatigue, breakage and arcing, both of which can start fires.

It's a lot to sort out. Mark the wires.

They sell 5-packs of colored electrical tape for about $5 at the hardware store. Typically blue red yellow green white.

So you might do something like this in box 1

and this in box 2

*The neutrals will be a wire from each cable that need be wire-nutted; I simply didn't bother drawing the wire nuts.

Note how the 2 travelers are color coded the same. That is because there is no need to distinguish travelers from each other.

I also spiraled the travelers' markings quite some distance, but the switched-hot only the width of the tape.

Now that looks super clear on the drawing, however in the box, things may be so confusing you need to mark the neutrals too. But you cannot use red, yellow or blue (hot colors) on a neutral wire, or you will inadvertently redefine it as a "hot" wire, which is wrong. White, gray and green don't have that problem. They won't redefine a hot because you're not allowed to redefine a hot to a neutral or ground. White and gray are neutral colors, and green won't redefine a neutral to ground, because that's not allowed either. So brace for an argument with the inspector, but I say using white, gray or green on both hot and neutral does not change the purpose of the wire, therefore is only marking for identification.