SUMIFS with multiple AND and OR criteria. How?

I would like to create a SUMIFS formula with the following criteria:
Criteria A AND Criteria B AND Criteria C AND Criteria D OR Criteria E

The sum range is A2:A10000.
E1 is a header row. The header is "TIME".
Criteria D is the target cell of the range E2:E10000 is empty.
Criteria E is the target cell of the range E2:E10000 is greater than cell G2 (9:00 AM).

Currently what I think I could do is:
=SUMIFS(Criteria A AND Criteria B AND Criteria C AND Criteria D)+SUMIFS(Criteria A AND Criteria B AND Criteria C AND Criteria E)

There is a lot of repetition (bold part). I wonder if there is any way to simplify it.
Thank you.