I was wondering if it makes sense to achieve a 4 inch foam exterior by - facenail 1 2x4 at the sill - sandwich a 1 inch 2x4 strip of foam board cut up. - facenail another 2x4. - do the same at the top plate now we are out 4 inches. fill the gap with foam boards. Then furr it up/create our rainscreen by facenailing 2x4's 16 inch oc. seems like it would provide a good nailbase siding and furring up the exterior this way seems easier then messing around with long screws. not sure facenailing them is enough without some screws between top /bottom. i suppose flipping them into stud position would solve that problem but then fastening at the bottom is the pain. not planning on doing this just wondering why ive never heard of it? btw this would be extending out beyond the foundation. its not a true double wall and only the openings would line up

It's more commonly done with 1x4 furring through screwed to the studs rather than 2x4 top & bottom plates. A simple top & bottom plate for attaching the nailbase doesn't of or long nailing the nailbase to the structural sheathing through 4" foam doesn't provide much structure, but you might be able to hire an engineer to specify a nail or other fastener and spacing that would be good enough.

Building on a Larsen Truss and filling it with fiber insulation is a standard retrofit similar to a double-studwall. For new construction it's somewhat more complicated than a double studwall, but as a retrofit it's easier than gutting the interior, and it doesn't reduce the usable floor area indoors. See:

https://www.greenbuildingadvisor.com/article/all-about-larsen-trusses

i was thinking of a way to just shoot nails, instead of screws. nah not a retrofit. thanks for that link thats exactly what i was looking for when i posted. for a new construction go with a double studwall? even if the plan is foam? I guess then just fill it with fiber.

Just looking for a way to attach the foam without screws but the more i research about building construction is most thing i think of have already been figured out or just dont work any better

is there an equivalent for roofs? i mean, how do you get 6 inches of foam there and still have something to nail to...thanks

In a lot of what I've seen for roofs, you basically just lay out the foam and screw it down to the plywood deck.  You use some sort of plastic washer system, be they standard flat washers or prong washers, to grab the surface and prevent tear-outs.

https://youtu.be/jaa3dgnMyXw

Then a P&S membrane.
Then furring (either vertical (straight down the roof) or cross-hatched at a 45 degree angle) screwed down into the rafters.  This gives you the necessary air gap to prevent your roofing from baking (and melting) the insulation.

Once everything's encapsulated, you really shouldn't have to worry about tear-out or disintegration as you're not putting THAT much of a point load on the foam "deck".  And the area any given screw has to hold is relatively small over the entire "field" of the roof.

If you're REALLY worried about it, you could use foam-safe construction adhesive to bond the various foam layers together as they're individually screwed down.