A challenge? - I always love a challenge...

So, the question was: how to make a three-layer weave, with warp-wise layer changes?
(and preferably on 12 shafts "only")

This is how I approached the problem:

(To all Swedish readers (and Ellen: hi, Ellen!): note that all tieups are for rising shed. This means that the layers/colours will be reversed if the tieup is used "as is" for a CM.)

Started with a three-layer (three independent layers) weave - for plainweave layers, that takes six shafts.
For instance like this:

(To make things clearer in my mind, I threaded the first (turquois) layer on shafts 1-2, the next (purple) on shafts 3-4, the third (red) on shafts 5-6. When the construction is ready, the threading can be rearranged for easier threading.)

I made the top layer turquoise, the middle layer purple, the bottom layer red-orange. The three layers do not interact at any point. (Note that the difference in nuances between warp and weft makes It easy to see that the bottom, red-orange, layer has a correct interlacement, even without using the "back view".)

Now, we wanted a lengthwise (warpwise) layer exchange. I decided the left hand side is a good place. Thus, to start the construction, assume another "block" of the same threading and colour to occur at the left side. Like so (left pic):

The same threading on a new set of shafts (= a new block), with the same colour order. We want to shift the layers, so I let them "cycle": the middle, purple, layer goes on top - the bottom, red, goes in the middle and the top, turquoise, layer has to go to the bottom.

OK, I hear you: how do I do this?
I am using Fiberworks PCW (silver, if that matters).
By clicking in the drawdown, I can get ends/picks to the top (for instance).

Middle pic above: all purple threads, both warp ends and picks, are taken to the top.
Next is to fix the interlacement: right-hand pic above. Note that the interlacement should be a continuation of the purple plainweave in the right-hand (first) three-layer block.


Now to fix the middle layer, the red-orange one. Click all ends and picks so that they are under the purple layer, but on top of the turquoise (left picture below). Fix the interlacement - easy because of the difference between the red and the orange - right-hand picture below.

For the bottom (turquoise) layer, it is easier to use "back view".
As it happens, all turquoise threads are already at the bottom... fix the interlacement, go back to "front" view again:

Unfortunately, all the 12 shafts are now used.
As we want another stripe, we add another block (6 shafts) - now the total is 18.

The same procedure again: make the red-orange layer top, the turquoise will be in the middle and the purple layer will go to the bottom layer:

In the hopes that I had missed something important, I let the software analyse my result - alas, I had not: it really takes 18 shafts to do this.

But...

What if: let one of the layers stay in the same position for two stripes: this will reduce the goal to two blocks. With the three "open" layers on the right-hand side of different widths, and several narrow-ish stripes on the left-hand side... voilà, only 12 shafts. An alternative?

(As I, personally, prefer straight threadings whenever possible, I rearranged it for this final picture, showing both front and back:

(Remember: click pictures to enlargen)