Hi,
You will have to manually drag n drop the dimensions to build an alert. There is no "one click" operation that could be performed to build the alert for all the sub dimensions (classifications).
To help select multiple dimensions and drag-drop them together in alert builder, you can select one dimension from left panel and then hold Shift key to select other ones. Once you've selected all the required dimensions, drag them together to right hand side alert builder.
Hope this helps!
Thanks,
Saumya