Yes this is possible. You can use a parameter to swap different fields and show the chart with different dimensions or measures. This will give a read-only viewer a way to explore different dimensions.
This training shows exactly how to do that:
Download the training solutions workbook and go to the last example.
The basics consist of using a calculated field with a case statement based on a parameter:
CASE [Choose Measure] --the parameter
WHEN "Coffee Gross"
THEN [Coffee Gross Sales]
WHEN "Coffee Profit"
THEN [Coffee Net Profit]
WHEN "Tea Gross"
THEN [Tea Gross Sales]
WHEN "Tea Profit"
THEN [Tea Net Profit]