I am using a formula such as ...

=IF(ROWS(H$15:H15)<=COUNTIF(A1:E9,$F$15),INDEX(A$1 :A$9,SMALL(IF($B$1:$B$9=$F$15,ROW($B$1:$B$9)-ROW($B$1)+1),ROWS(H$15:H15))),"")

However I am having serious trouble getting this to work across many columns
and display ALLL results in one column. Can I modify this formula, or go
about this in another way ?

A field example of this formula is

DOG 1 CAT 1 1
CAT 0 PIG 1 2
PIG 0 DOG 0 3
COW 1 COW 0 45
DOG 0 MOOSE 1 56
PIG 0 DEER 0 7
CAT 0 COW 0 8
DOG 0 DOG 0 9
PIG 1 CAT 0 10

Starting at A1