you just need 2 -
a habitable with organics & farmland for mining, light ind & farming.
and a very hot +3/+3/+2 (think this can happen naturally, not 100% sure though) no atmo planet for fuel prod, mining, refining, heavy ind & high command.
Yeah, the +3/+3 hot worlds always have dense or toxic atmosphere, and they can't also have volatiles. So in a natural setting you would need a third planet with no atmosphere and volatiles, I believe these are most often cold planets.
Of course, if you want to use the item that boosts volatiles production you would instead need a gas giant (which also has dense or toxic atmosphere). You can probably get by without it, but given condition #2 I would say you need a total of 4 planets.
1. Habitable planet, organics, farmland, preferably minerals,
no transplutonics (mining, light industry, farming, commerce)
2. Extreme heat, +3 minerals, +3 transplutonics (mining, refining, heavy industry, fleet command)
3. No atmosphere (fuel production)
4. Gas giant, +2 volatiles, preferably
not high gravity (mining)
You want the commerce on the habitable world because the hot world (tectonics) and gas giant (gas giant) won't be able to install the spaceport item for increased accessibility. You could put it on the no atmosphere world, but that light industry with open port is gonna be making way more bank than what you can get from some space rock. With 5 industry slots you still have room for tech mining on every planet, but I don't think gas giants or extreme heat worlds have ruins. Ideally the space rock would have minerals and volatiles but they're never going to be +3/+3 like your hot world, so aside from trading fleet command for fuel production it's going to be an inferior imitation of your hot world. You can squeeze in heavy industry on both the gas giant and the space rock to up your maximum production per month and beyond that I dunno.
Another thing you should look for is if the planets orbit the gas giant, that way it's much easier for patrols to protect all of them.
*Edit*I guess gas giants can be hot, but I don't think I've seen a hot one with +2 volatiles nor have I seen one with extreme heat at all. If it exists, maybe it can be a military base. With a little cheating we can get something like:
1. Habitable planet, organics, farmland, minerals,
no transplutonics (mining, light industry, farming, commerce, tech mining)
2. No atmosphere, +3 minerals, +3 transplutonics (mining, refining, heavy industry, fuel production, tech mining)
*impossible without cheating3. Gas giant, +2 volatiles, extreme heat,
not high gravity (mining, refining, heavy industry, fleet command, commerce)
*impossible without cheating(?)Putting commerce on the military planet helps balance out the stability penalty, but if you only get one I would still stick to the habitable planet. Also, having a proper comm relay (not makeshift) would be good.