Foam board wall detail question (trying to do the “right” thing)

Hello!
I have been lurking here for some time and have found many answers through the wealth of knowledge that is provided here! However, I am stumped which has led me to my very first post here. So please, forgive me in advance and go easy on me.
I live in Climate zone one specifically hot and humid southern Louisiana. I just moved into a new home last year. While it is new to me, it was built in the late 1980s. It has wood siding and a double skillion roof and I imagine was pretty modern for it’s time.
The wood siding is long over due for a paint job and I really want to upgrade to some type of Hardie board siding. My initial plan was to leave the current wood siding and come on top with some rigid foam board to get me better sealed up and insulated. However, upon looking under my siding I came across some perplexing things I had not seen.
There is plywood under my wood siding and rigid foam board under it and attached to the studs! I believe it is Rmax foam board because that is in my attic. I thought it was their structural foam board, but after talking to their tech support they do not know if that was even available int he late 80s. They were however pretty surprised that it was there for my homes age (maybe it was ahead of its time).
So, my concerns and questions about my scenario are as follows:
Is there any situation in which I can add more foam board with my current setup? (I was going to take down the siding and then add, but then found the plywood)
Would I be “sandwiching” siding or plywood between foam boards?
My only initial concern for me was trapping moisture in my climate, but after speaking with Rmax support they kept emphasizing the importance of fasteners, their lengths, and their penetrations to the studs.
Sorry for the length of this, but I wanted to be as clear as possible for a newbie. Any help or guidance is appreciated!
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Replies
Sandwiching plywood between two layers of foam can add some risk to a wall. You've lessened the drying potential of the plywood should water find its way into the first foam layer. That being said, you may be able to reduce this risk by making the wall sheathing the location for the water resistive barrier (WRB) and install a WRB product that allows for drainage. Something with dimples or ripples. Another option would be to use an insulation product that has built-in drainage, like some of the InSoFast foam panels.
Hope this helps,
Randy