I am assuming that you would like to have a chart with 2 bars showing for each dimension value. Once bar being the sum of sales by month and the other one being sum of sales by category(You need this bar to have stacked colouring based on the no of categorys). This is not possible with the visualizations implicitly available in Sense.
You do have the leverage to build your own visualizations. So its never the dead end.
So the answer is no(with the in-built visualizations) but Yes if you are willing to go with an extension.
AS sangram says its not out the box functionality. I've done a chart that switches itscontent based on a variable set by the user using a button. Perhaps this might help. Makes Sense to go round in circles
Not sure if I understand your requirement.
To me, it seems you have ONE measure, something like
and TWO dimensions, Month and Category.
If this is the case, a stacked bar chart (Month on x-axis, Category as stacked segments) should be available with Sense charts out-of-the box. Just use two dimensions and choose the stacked representation style on presentation tab.