Magazine Puzzle Fun

When I add this Brasilian Domino Stamp to my collection I thought of this puzzle.
The objective is to include the most quantity of pieces with this conditions:

1)You add a new piece as in domino, same number with same number

2)Pieces can not touch with others (except of course the one you are joining)

3)The sum of the numbers in each row and column should be always different

For example in the stamp the first piece is 1-3, so the columns are 1 and 3, and the row is 4. The second piece is 3-2 so the columns are 1 and 8, and the rows are 4, 3 and 2. The third piece is 2-5 so the the columns are 1, 8, 2 and 5, and the rows are 4, 3 and 9, we have numbers 1,2,3,4,5,8,9 all differents.

Other example:

The first piece is 3-4, so the columns are 3 and 4, and the row is 7.

The second piece is 4-2, the columns are 3 and 10, and the rows are 7, 4 and 2.

The third piece is 2-2, the columns are 2, 5 and 10, and the rows are 7, 4 and 6.

This is NOT a valid position because pieces 3-2 and 3-4 are in touch.

The fourth piece is 5-3, the columns are 2, 13 and 10, and the rows are 5, 3, 7, 4 and 6.

The fifth piece is 5-1, the columns are 2, 13, 15 and 1, and the rows are 11, 3, 7, 4 and 6.

In this case I think it is not possible to add the sixth piece.