MAX Over A Set Of SUMIFS

I'm trying to find the maximum over a set of conditional sums, preferably using an array formula or some other single cell solution. My experience with array formulas so far has been to copy things off the internet and modify slightly to my needs.

Here is how my data is set upA

B
C
D

Trait1
Trait2
Value
Trait 1 to Max over

Cat
LongHaired
3
Cat

[code]....

The "Trait1" I am summing over will remain constant for each refresh of the spreadsheet. I want to return the max value of the sum over each "Trait2" that falls into the "Trait1" category.

In this example for Trait1 of "cat" I would return 8 (5+3) that corresponds to LongHaired cat.If I were writing straight SumIf and then Maxing over I would write

Code:
=SUMIF(C:C,A:A,$D$2,B:B,"LongHaired")

for each unique Trait2 and then Max over the set of outputs.