If I understand your question you want to be able to select Corporate for example from sheet 2 filter the map below then when you change the dimension shown to region with the parameter retain the filter for corporate. So trying to retain action filters instead of using the quick filter on the right side.
The short answer is you can't and I think that is a good thing. Retaining action filters in a view with no visual indication of what is filtering the chart could quickly lead to confusion. So you would either need to display both sheets to allow for an action filter that uses a combination of segment and region or use parameters/filters to restrict the view with the options listed at all times.
A slightly more complicated option is to force the user to first select a segment then pick from a list of regions. In the attached workbook I have set this up and use an action filter to hide the second list until a selection has been made. Changing the Dimension in the parameter now changes the selection order. I believe this is close to the functionality you are looking for.
When I select Corporate from sheet 2, I want the quick filter on the right to also automatically select Corporate. If I had 10 dimension/parameter options, I would have to scan the list of quick filters on the right to find the one that corresponds to Segment and then select corporate. Clicking corporate on the sheet is an alternative. I suspect this cannot be done (at least easily), but would like someone to confirm.
If you have 10+ options you should just list them out as filters. Once I start trying to add more than 5 filters though I try to take a step back and rethink what I am trying to do with the dashboard. Using only relevant values might make some of the lists easier to read but could slow down the dashboard.