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What Aaron said is true, but you might also consider using the parameter to drive visible sheets within a single dashboard (see Creating a Sheet Selector for a Dashboard | Tableau Software) Using this technique could feasibly allow you to completely change which views are shown in your dashboard based on which parameter value is selected.
Thank you both for the tips. I might submit this as a suggested feature.
The sheet selector approach may not work. The entire interface needed for the "All" option is very different than the one needed for the remaining items. In addition to changing the sheet that is shown, I would also need to change navigation and other elements. I'll give it a try, though.