Recently it has been observed that the numbers of 2-crossings and 2-nestings have a symmetric joint distribution over many combinatorial structures, including permutations, matchings, set partitions, and linked partitions. These results have been put by Kasraoui in the larger context of enumeration of northeast and southeast chains of size 2 in fillings of moon polyominoes. In this talk we present much stronger symmetric properties of northeast and southeast chains. Our results are obtained by generalizing the polyomino model in two ways: (1) The polyomino is equipped with a charge function, and (2) We relax the constraints on the polyominoes to allow a full action of the symmetric group. This is a joint work with Andrew Wang and Jean Yeh.