Warning: This is the first time that I attempt to modify OpenXCOM code/data, so I am still a bit uncertain.
I have attached a rule file that replaces the "Plasma Needs Elerium" mod for use with the "Expanded Alien Armoury" mod. Basically, it adds the research restrictions to the new EAA weapons as defined in the alien armory. I created the dependencies depending on the weapon type:
Plasma pistol -> Plasma Caster
Plasma rifle -> Plasma Sniper Rifle
Heavy Plasma -> Plasma Blaster
Also keeping the progression already present in the PNE mod:
Plasma pistol -> Plasma rifle -> Heavy Plasma
and the clips requiring both the gun research and the previous clip (except for the pistol clip which only requires the pistol by current PNE mod).
A quick test using one of my saved games shows that it works well, but this is my first try at a mod, so it might well not work exactly as intended. I removed all the "unlocks" statements from the rulefile as well. I originally kept them, but found out that they seem to forcefully unlock research topic, even though some other requirements are not met. Specifically, having the guns unlock their clips bypasses the need for the previous clip to be researched. You could, for example, research:
Elerium -> Plasma Pistol -> Plasma Rifle -> Heavy plasma -> Heavy Plasma Clip
and bypass the pistol and rifle clips. With the "unlocks" statements gone, you need to research all the dependencies and will get the "new research topic" message at the right time: When you have researched all the prerequisites. I am not sure what the "unlocks" statements are supposed to be for, to be honest...
I kept everything out of the EAA mod, as that is already quite a large mod with lots of information and a clear aim: Give more weapons to aliens. And it does that it very well. Conversely, it fits the aim of the PNE mod rather well to be adapted to new plasma weaponry, so now there is an "Expanded Plasma Needs Elerium" mod.