Excel conditional SUMPRODUCT / SUMIFS / Array Formula for optional dimension - excel

Question

I have a sheet of data with multiple dimensions like this:
A B C D E
1 COUNTRY FLAVOUR SIZE DATE SALES ($)
2 Japan Strawberry 100ml 10/12/14 100
3 Japan Banana 100ml 10/03/15 100
4 China Orange 200ml 14/04/15 30
5 France Strawberry 200ml 11/04/15 400
6 UK 200ml 23/04/15 250
7 ....
I want to aggregate this data over a date range, where the summary sheet has each dimension (country & flavour), and if I do not specify a dimension it sums all rows for that dimension.
A B C
1 COUNTRY FLAVOUR SALES TOTAL
2 Japan Strawberry 100
3 Japan 200
4 Strawberry 500
I can do this if all the dimensions are present (i.e. row 2 above) using a SUMPRODUCT or SUMIFS:
=SUMPRODUCT((data!A$2:A$100=A1)*(data!B$2:B$100=B1)*(data!D$2:D$100>[start_date]*(data!D$2:D$100<[end_date])*(data!E$2:E$100))
However I have not been able to figure out how to include all rows for a dimension if that input cell is empty (e.g. row 3 above). I tried:
Adding an IF statement or OR statement within the criteria (e.g. OR(data!A$2:A$100=A1,isblank(A1))).
Using a + in a SUMPRODUCT as an OR statement, (per this answer https://stackoverflow.com/a/27536131/1450420)
One solution is to have different branches of the formula depending on which summary dimensions are present, but that would quickly get out of control if I extend this same behaviour to further dimensions like Size.
Any help appreciated!
(I'm running Excel Mac 2011).
EDIT
Per #BrakNicku's comment one of the formulas I tried was =SUMPRODUCT(((data!A$2:A$100=A2)+ISBLANK(A2))*((data!B$2:B$100=B2)+ISBLANK(B2))*(data!E$2:E$100))
The reason this doesn't work is that sometimes my data has blank attributes (edited above). For some reason this formula double-counts rows where the attribute present matches (e.g. data!A6) but the other attribute is missing (e.g. data!B6).
EDIT 2
I can see why this double-counting is happening, because the + is summing the match because data!A$2:A$100=A2 (they match because they are both blank) and the match because ISBLANK(A2) (it is indeed blank). The question would remain how to achieve this without double counting. If needed a workaround could be to fill all blank cells on my data with some placeholder value.

Answer 1

The reason for double-counting values is here:
((data!A$2:A$100=A2)+ISBLANK(A2))
If a cell in A column is blank, both parts of this sum are equal 1. To get rid of this problem you can change it to:
(((data!A$2:A$100=A2)+ISBLANK(A2))>0)

Answer 2

Try this (I only included the first two, I left the dates out):
=SUMPRODUCT((((Data!$A$2:$A$5=A2)+(A2=""))>0)*(((Data!$B$2:$B$5=B2)+(B2=""))>0)*(Data!$E$2:$E$5))