Is there a way to chroma key 2 different colours at the same time?

I believe that you can only have 1 Chroma Key: Simple filter on a clip and only 1 Chroma Key: Advanced filter. If you have both then the last one you applied is the one used.

You can try changing the “Distance” parameter of the CK: Simple filter to include more colours similar to the one you chose. The CK: Advanced has far more control of the colours included, so I would experiment with that.

Is your greenscreen a video of a person talking with little movement? If so take a look at this post for a possible solution: