duplicating your worksheet is currently the only route I know of to accomplish what you are looking for.
OK, thanks for that Joe. I think Tableau Server doesn't have the sheets behave like this, but I haven't tested that yet.
I'll put in a suggestion I think.
Inspired by Mike's 'workaround', I find a solution to eliminate the impact of Global filter on other dashboard and the constraint of multi-select.
1. Create a set in the worksheet that is going to be in the secondary dashboard. For example, if my primary dashboard is about the sales of all regions in US and my secondary dashboard is one of the region (Northeast as an example), I would create a set named Northeast and select the value of Northeast from Regions under Dimentions.
2. Drag the set (Northeast) to Filters in the sheets that would be in the second, third.....dashboard.
In these ways, the set at the local filters defines the Region which you want in the specific sheet and won't be impacted by the global filter even though it's still in the filters shelf.
Hope it helps.
Don't be hesitate if you have any question.