Yes, a third state is supported natively by MacOS. Quote from Apples Human Interface Guideline:
Use a mixed state when it makes sense. A checkbox should accurately reflect its state. If a checkbox is used to globally enable and disable multiple child checkboxes, it should show a mixed state—reflected by a dash—when those children are not all in the same state.
You will need to create your own button class to achieve this. Either using a FMX styled button that adds the tri-state option. Or a FMX wrapper around a native button. If you want to go native, you can use the TMS mCL component suite, which is not free though.