Sum of Categories by Record across Multiple Worksheets

In the following formula, A11:A17 contains names of various clients, of which there are hundreds. A4 refers to a specific cell on the first sheet of the workbook into which I could type a specific client name as needed. A11:A17 is varying quantities. I want to be able to type the client name into cell A4 and have the formula then calculate the sum of A11:A17 throughout the entire workbook.

=SUMIF(A11:A17,A4,B11:B17)+SUMIF(Sheet2!A11:A17,A4,Sheet2!B11:B17)+SUMIF(Sheet3!A11:A17,A4,Sheet3!B11:B17)

The above formula works fine for a limited number of worksheets. The workbook I'm trying to work with is over 40 sheets, however. I've tried both DSUM and SUMIF with limited results. They both resist 3-D references. Insert>Name>Define doesn't seem to help either. I have to asume that there is a more elegant way to achieve this calculation, but my knowledge of Excel is execrable. Your help is greatly appreciated.

I have attached a zipped Excel file that I'm using as a test.