Is there any way to have more than one Row Label in an Excel Pivot Table construted using Multiple Consolidation Ranges?

When creating a Pivot Table from a single data source, all the relevant column names are listed in the Pivot Table Field List, but when the data is from multiple sheets, only Row and Column are listed as available fields in the field list.

I would like to be able to have 2 or 3 Row Labels in my pivot table, but I can see anyway to achieve this.

Does anyone know if it is possible to do?