I had posted a counting and summing question here a couple weeks ago and
received a great answer and introduction to the sumproduct function. I'm
looking for one more item, this one extracting the largest number from a
range but only if conditions are met for other ranges.

The help I received before with the sumproduct function allowed me to count
and sum results from cell ranges e1:e10 when conditions were true in ranges
a1:a10, b1:b10, c1:c10 and d1:d10. So if a4, b4, c4 and d4 conditions were
true, i was able to count e4 and sum e4. Same for row 6, etc.

What I'm looking for is a way to identify the largest number in e1:e10 when
the first four conditions are true. Thus, in my previous example, if e4 was
10 and e6 was 6, I want my result to be 10, even if e8 [which should be
ignored if there is a false condition in a8, b8, c8 or d8] is 15. I have
tried working MAX or LARGE into some IF functions, but it would always return
the largest number [i.e., 15 from e8] in the whole range rather than the
ranges with true conditions.

Is what I'm looking for possible? Did this make sense?

Thanks in advance.