Sure.
Here's how the Italian jury result during last year Annual Contest, using the traditional method.
J1
J2
J3
J4
J5
TOT
IRL
9
8
8
11
2
38
NZL
8
1
5
12
3
29
CRO
1
9
12
7
29
LTU
10
6
4
20
BRA
10
2
2
5
19
TUN
11
5
3
19
NED
7
12
19
CHN
9
9
18
SVK
7
10
17
ALG
10
7
17
ESP
7
9
16
GER
2
12
14
Now here how I propose it could work:
1) First every song receiving the maximum 12 points should be ranked.
J1
J2
J3
J4
J5
TOT
CRO
12
12
GER
12
12
NED
12
12
NZL
12
12
POL
12
12
2) As we can see, last each jury member chose a different "winner" song. So in this cases the first tie breaking criteria would be total number on individual juries voting for them, which will result in something like this:
J1
J2
J3
J4
J5
TOT
JV
NZL
8
1
5
12
3
29
5
CRO
1
9
12
7
29
4
NED
7
12
19
2
GER
2
12
14
2
POL
12
12
1
3) Then we can see there's still have a tie between the Dutch and German entries. So, the next criteria to apply would be which of those received the "bigger" points, resulting in the Netherlands' song beaing ranked third and Germany's fourth.
As you can see at this point, Poland's entry which wasn't originally ranked, yet was deemed the winner by one individual jury would still receive some decent points.
4) Then we will repeat the same process with those songs ranked second by the individual juries:
J1
J2
J3
J4
J5
TOT
JV
IRL
9
8
8
11
2
38
5
TUN
11
5
3
19
3
DEN
3
11
14
2
AUS
1
11
12
2
COL
11
1
12
2
5) Now, Australia and Colombia tie can't be broken by the factors explained above, so a random draw would take place to rank them.
6) Then the same process would be repeated with songs ranked 3rd, then 4th and so son, if necessary.