I don't know of anyway you can do this via filters. But I have done something like this using calculated fields.
To do this you create a calculated that returns 1 if it matches your criteria and 0 if it does not for each "count" you are looking for.
IF [Gender] = "male" THEN 1
IF [RaceEthnicity] = "White" THEN 1
Then you can just add all your calculated fields as columns. SUM(<CalclatedField>) is same as count.
If you need a separate set of filters to act on the additional column you should create the column as an additional worksheet and place it to the right of your current worksheet in a dashboard.