Stacking teleconverters usually isn’t a good idea if your goal is image quality. Each teleconverter adds optical degradation, and stacking two tends to make sharpness worse still. With inexpensive teleconverters, the odds of getting a strong result are fairly low.

There’s also a practical risk that stacked converters may prevent focusing at infinity, which is obviously a problem for the moon.

Because the moon is bright, exposure is less of a concern than sharpness and focus. In practice, you’ll often get better results from a single teleconverter at a more modest focal length—around 500–600mm was suggested—and then cropping, rather than stacking converters to reach extreme focal lengths.

That said, if you already own or can borrow the gear, it can be a fun experiment and may produce usable results. But it’s not something to buy another teleconverter for with high expectations. As a practical recommendation: try the 200mm lens with your existing 3x teleconverter first, and if you want more reach, compare that result with cropping before spending more.