How to apply hasAll() to multiple selection tags and fields

I am basing my code off of this tutorial: https://www.wix.com/corvid-examples/selection-tags
My use-case is slightly more complex, in that I want to have at least 2 separate SelectionTag elements. In my case I am using GameType and Language. I want people to be able to filter by either multiple GameTypes, multiple Language (its language target, not spoken language) or some of both.
I want it to be hasAll and not hasSome, because the result should be the intersection of the categories.
In my database, there is a GameType and a Language field, both of type Tag. I could combine all filters in one DB column, but on the front end I want different categories to be different colors and to have title text above each one telling the user what the selection buttons filter.
I thought the answer was going to be to group all my selection tag elements together and set an onChange() to that group, but it won’t let me