I'd have a structural engineer out to have a look at your project and to draw the plans you will need for permitting.

https://www.houzz.com/discussions/6405591/stacking-attic-and-ceiling-joists

My house has some sistered joists. No plywood in between. They are under the porch, where plywood might not last well, though.

You need an adequate fastener schedule, not an engineer.

Typically the plywood is used as a spacer to get the width required. Let us say you want a 4 inch wide beam but since framing lumber is 1-1/2 inches wide, (2) will only get you a width of 3-1/2 inches. To get 4 inches a half inch spacer of plywood is used between the two.

But not always.

Sometimes to get the proper load bearing properties of a beam, plywood is used since it is stronger than framing lumber per given size. Calculating load bearing capabilities then gets kind of tough so its best to get an engineer if you are up against it as far as room constraints and have heavy loads to withstand.

"I rarely frame walls with 2x4s, but when I do, I use 1⁄2-in. rigid foam between the plies of built-up headers rather than OSB or plywood. Even though the R-value of the foam is small, it breaks the thermal bridge somewhat."

If plywood or OSB contributed any required structural strength, they certainly couldn't be replaced with rigid foam.

Huh... if the two 2X4s were adequate by themselves, inserting OSB and then replacing the OSB with foam would not allow your conclusion.

You should read Travis Johnson's Post - particularly the second paragraph.