You can inspect and see the class for up and down arrows (In both classic and touch UI). You can write click event on both up and down arrows which will re arrange the items and have your custom logic in side that captured click event.
Below is sample code for classic UI.
$('.cq-multifield-up').on('click', function(evt) {
//custom logic will go here.
});
$('.cq-multifield-down').on('click', function(evt) {
//custom logic will go here.
});