You can use a formula that adds the different Sumifs together. For example:
=SUMIF(B4:B12,"a",C4:C12)+SUMIF(B4:B12,"b",C4:C12)+SUMIF(B4:B12,"c",C4:C12)
This would sum A, B, and C.
If I understand your question, you need to use an array. I usually use something like this:
Column A contains names of cities, column B contains names of people, and column C contains amount of sales. If you want to see how much sales Mark had in Cleveland :
{sum((a1:a100 = "Cleveland")*(b1:b100 = "Mark")*(c1:c100))}
The outside parentheticals are not actually typed. When you type the formula, you must hit Ctrl + Enter. This makes the formala an array.
Hope this helps.