Hope I've understood what you need.
To avoid very complex array formulas i suggest a helper column (gray area)
[TABLE="class: grid"]
<tbody>[TR]
[TD="bgcolor: #DCE6F1"][/TD]
[TD="bgcolor: #DCE6F1"]
A
[/TD]
[TD="bgcolor: #DCE6F1"]
B
[/TD]
[TD="bgcolor: #DCE6F1"]
C
[/TD]
[TD="bgcolor: #DCE6F1"]
D
[/TD]
[TD="bgcolor: #DCE6F1"]
E
[/TD]
[TD="bgcolor: #DCE6F1"]
F
[/TD]
[TD="bgcolor: #DCE6F1"]
G
[/TD]
[TD="bgcolor: #DCE6F1"]
H
[/TD]
[TD="bgcolor: #DCE6F1"]
I
[/TD]
[TD="bgcolor: #DCE6F1"]
J
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
1
[/TD]
[TD]
ID
[/TD]
[TD]
Year1
[/TD]
[TD]
Year2
[/TD]
[TD]
Year3
[/TD]
[TD][/TD]
[TD]
Criteria
[/TD]
[TD]
Count
[/TD]
[TD]
List
[/TD]
[TD][/TD]
[TD]
Helper
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
2
[/TD]
[TD]
J North
[/TD]
[TD]
Corn
[/TD]
[TD]
Hay
[/TD]
[TD]
Barley
[/TD]
[TD][/TD]
[TD]
Corn
[/TD]
[TD]
3
[/TD]
[TD]
J North
[/TD]
[TD][/TD]
[TD="bgcolor: #D9D9D9"]
3
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
3
[/TD]
[TD]
M North
[/TD]
[TD]
Hay
[/TD]
[TD]
Barley
[/TD]
[TD]
Corn
[/TD]
[TD][/TD]
[TD]
Hay
[/TD]
[TD][/TD]
[TD]
M North
[/TD]
[TD][/TD]
[TD="bgcolor: #D9D9D9"]
3
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
4
[/TD]
[TD]
N North
[/TD]
[TD]
Barley
[/TD]
[TD]
Corn
[/TD]
[TD]
Corn
[/TD]
[TD][/TD]
[TD]
Barley
[/TD]
[TD][/TD]
[TD]
M South
[/TD]
[TD][/TD]
[TD="bgcolor: #D9D9D9"]
2
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
5
[/TD]
[TD]
J South
[/TD]
[TD]
Corn
[/TD]
[TD]
Corn
[/TD]
[TD]
Corn
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD="bgcolor: #D9D9D9"]
1
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
6
[/TD]
[TD]
M South
[/TD]
[TD]
Barley
[/TD]
[TD]
Corn
[/TD]
[TD]
Hay
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD="bgcolor: #D9D9D9"]
3
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
7
[/TD]
[TD]
N South
[/TD]
[TD]
Corn
[/TD]
[TD]
Barley
[/TD]
[TD]
Corn
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD="bgcolor: #D9D9D9"]
2
[/TD]
[/TR]
[TR]
[TD="bgcolor: #DCE6F1"]
8
[/TD]
[TD]
J East
[/TD]
[TD]
Pasture
[/TD]
[TD]
Corn
[/TD]
[TD]
Barley
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD="bgcolor: #D9D9D9"]
2
[/TD]
[/TR]
</tbody>[/TABLE]
Formula in J2 copied down
=SUMPRODUCT(--(COUNTIF(B2:D2,F$2:F$4)>0))
Criteria in F2:F4
Formula in G2
=COUNTIF(J2:J8,3)
Array formula in H2 copied down
=IF(G$2>=ROWS(H$2:H2),INDEX(A:A,SMALL(IF(J$2:J$8=3,ROW(J$2:J$8)),ROWS(H$2:H2))),"")
Ctrl+Shift+Enter
M.