Absolutely possible.
Create a stacked bar chart with the measure that you want, then add the regions as the columns, and the dates as the rows.
The built in percentage labels will only work for the 100% stacked bars so you will need to create a formula measure. Create a formula measure with a formula like PERCENTTOTAL($<measureName>$, $<regionName>$). This will create a measure which is the percentages which we can use for the labels.
In the chart properties, click on this new measure and in the 'main' tab, uncheck 'visible'.
Go back to the chart properties, and click on the original measure, and go to text, data label settings and type '[' in the text box, then select the percentage measure name. Set the position to be 'inside'
To create the total at the top, create a new formula measure with a formula like SUM($<measureName$,<$DateName$). Go to the chart properties and click on that measure.
Set the 'chart type' to 'point', then go to the 'look' tab and set the 'marker height' and 'marker width' to 0.
Go to the 'text', 'data label settings' and type '[' in the text box, then select the Sum measure name. Set the position to be outside.
Hope this helps, let me know if you want me to clarify or add anything.
Thanks