They do include notes in the installation instructions for the TBIII along the lines of "The Themobalance III valve requires a Thermbalance III trim kit. Do not attempt to use any other trim kit with this valve."

You could also call their tech service and ask.

Stops are generally required in commercial buildings and apartment buildings, etc, where it would be impractical to turn off a portion of or the entire water supply to work on one valve in one apartment. The stops allow the building's water to remain on while working on the valve. They can certainly be used in residential, I've done it several times.

I usually control water flow to individual areas in a house with full-flow 1/4-turn ball valves in the basement. A set for the kitchen. A set for the bathroom, etc.

Thanks mongoct! Your posts have been so helpful as I shopped for the Hansgrohe shower stuff. It sounds like I should go for the stops as a convenience measure, unless I'm able to retrofit all the supply lines with valves for different sections of the house (what a great idea, but unlikely to happen in my vintage house).