summing an index(match,match) over multiple spreadsheets

Hello! First time user and poster. I've searched and seen several "indirect" functions but I still can't get a formula that accomplishes my goal.

This formula works for pulling info off one worksheet:
=INDEX(sheet!$1:$1048576,MATCH($A4,sheet!$A:$A,0),MATCH(C$2,sheet!$3:$3,0))

Now, I am trying to make this same formula a "sum" function over a range of worksheets (without having to simply add the same string above with each sheets name). The spreadsheets have to be index/matched because my two match criteria, month and account, are in different cell references across spreadsheets.

Any help would be appreciated!

Thanks,
Andy

=INDEX(abq:abq2!$1:$1048576,MATCH($A4,abq:abq2!$A:$A,0),MATCH(C$2,abq:abq2!$3:$3,0)) returns a "#value". If I do:
=INDEX(ABQ!$1:$1048576,MATCH($A4,ABQ!$A:$A,0),MATCH(C$2,ABQ!$3:$3,0))+INDEX('ABQ2'!$1:$1048576,MATCH($A4,'ABQ2'!$A:$A,0),MATCH(C$2,'ABQ2'!$3:$3,0)) I get a valid result. The spreadsheets are right next to each other.

Thanks for the quick response.

I am trying to avoid the second scenario because I'd like to be able to create worksheets and pull them in the worksheet range and have them roll into the consolidating worksheet. I just added the "longhand" version above to make sure I could get the right answer and show what I'm hoping to accomplish with a single formula. Over time, the workbook will have 30 worksheets that I'd like to consolidate.

Does that make sense?

Because all the worksheets have different references:

ie: in abq, the index/match combination may be cell d47. in abq2, the index/match combination may be cell e52.

All the worksheets have difference date ranges and different accounts as the worksheets represent different site budgets with different service offerings. I don't want to change every worksheet when I need to make a change to one.

Thanks for sticking with me. see cell c6 on Summary tab. I am trying to be able to create a formula that works for anything between the start and end worksheets and exclude anything outside that worksheet range.