A hansgrohe thermobalance III could run all 3 units, but only 2 at a time. One valve, one handle. Plenty of trim options.

Here is a link that might be useful: Thermobalance III

"I don't always want to run them all at the same time. I would prefer to be able to set them at different temperatures if that wouldn't be too expensive."

If you want different temp from each outlet, then you'd need a separate supply valve for each type of fixture. It sounds busy but it's actually quite simple to plumb. As far as expense, it may sound like a cop out but it all depends on what type of valve you chose. Symmons Temptrol makes excellent pressure-balancing valves for about $100. The trim kits aren't as sexy as some of the "fancier" manufacturers, but their valves are top-notch.

"Or if I have to "link" two of the systems, then the body sprays and the hand-held could be the same temperature so long as I can use them independently of one another..."

Then you could put the body sprays and handheld on a single supply valve; that valve can have a built-in A/B/AB diverter, or you could install an A/B/AB diverter independent of a simpler On/Off supply valve. You'd then need a second supply valve for the fixed shower head.

For what it's worth, in my shower which is 5' by 7', I have a hand-held on a slide bar and an overhead 12" rainshower head. We prefer them at different temps, so they are on two different supply valves. Easy to do. We had contemplated adding body sprays, but neither my wife or I are fans of them. Had we done that, they'd have been on a third supply valve.

It might seem obvious, but try to locate your valves just inside the shower where you can turn the water on without having to step into the shower, that way you can turn on the water without getting wet.

Lastly, run some flow volume numbers by adding up the flow of each fixture that might be on at the same time. Most bathrooms are plumbed with 1/2" copper supply tubing. If you're going to have all fixtures blazing to recreate a human car wash, then you might need to up your copper tubing to a larger diameter, 3/4".

If you do have a SINGLE valve controlling all those heads, then you'd want that supply valve to be 3/4" as well.

If you opted for two or more valves to control the heads, then you could still run 3/4" tubing from the water heater to the shower valves to get the needed volume of water to the shower, then step it down to 1/2" and use 1/2" valves and 1/2" tubing to distribute it to the heads.

You might find guidance, or sadly more confusion, by reading through this.

Mongo