I've wanted to do that many times myself, but I don't think it's possible.
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A work around is to make a copy of the dimension being filtered. Add that copy to the filter shelf with appropriate filters set. Then use the original dimension as the "quick filter" with "only relevant values" selected. This will result in only showing options in the filter that are selected in the copy.
Not sure if that makes sense or not.
Excellent work around, Thanks Dave.
No problem, it's an essential work around to 90% of my views.