You can use something like this in E2
=SUMPRODUCT(--(A2:A100=A2),-(B2:B100=B2),--(C2:C100C2),-(D2:D100<D2))
This will give you the count of rows where Col A has the value A2, Col B has
B2, Col C has C2 and Col D has D2.

You can add more terms for other columns...

"blswes" wrote:

I am looking to count the number of unique text cells in Col. A that meet
several criteria across Col. B-F.

And I'll want to do this calculation numerous times with changing criteria
(to fill out a large table).

Any ideas?