Forget plywood unless you can get T&G (with the T&G on all sides) and go for P5 T&G chipboard which comes in 2400 x 600 "planks"). Much cheaper and a lot easier to handle than plywood. I'd cover the existing sub-floor with a thin layer of polythene sheet, put the PIR over that (in a staggered "brick patternm"), then lay down another layer of thin polythene sheet over that before laying the chipboard. The first poly layer stops damp (but may not be necessary, your call), whilst the second at the top prevents glue squeeze out from laying the chipboards from permanently "welding" those boards to the PIR. The PIR is floated on top of the PIR, that is it is layed in brick pattern (with the joints staggered at half sheet point) and all the tongues are glued with D4 flooring glue (*normlly a polyurethane glue). To pull the joints up tight you can use flooring straps and a flooring pull bar. TBH I generally just get someone to stand on the first row, push the second row board into position against the first row, lay a 4 to 6ft length of 3 x 2 or 4 x 2 stud against the grooved (outer edge) of the board I'm fixing, stand with my legs apart, heels on the second board, toes on top of the stud, and gently tap the board into place - with a 7lb sledge hammer. Awkward bits and last rows will need a flooring pull bar and you will need some flooring (wedge) packers to give you a 5 to 10mm expansion gap around the perimeter. As you add more and more boards the friction of the floated floor means it will move less and less. Note that the floor flots and is not fixed to anything and that the spacer packers can be removed once you have finished
It may be best to ask the flooring guys what they prefer, but on many commercial jobs the floorers will screed a chipboard sub-floor with SLC before applying the LVT.
