Other option

window.KDJ || (window.KDJ = {});    //namespace
KDJ.controller = (function () {
    $(document).off('PAGE_DISPLAYED');
    $(document).on('PAGE_DISPLAYED', function (e, data) {
        if(data.customFunction !== undefined) {
            //do things if you want

            data.customFunction();

            //do things if you want

            // here I use the return to pass by the switch
            //you could use another property like if(data.useSwitch) => switch() or simply use an else clause
            return;
        }
        switch(data.pageId) {
            case "page1":
                // do something..
                break;
            default:

                break;
        }
    });

    return {
        // exported methods and props..
    };
})();


KDJ.view = (function () {
    // ...
    $(document).off('pagechange');

    //This object its optional, you could pass it explicitly everywhere.
    var pageDisplayedObj = {
        'pageId': loadedPageId,
        'key': key,
        customFunction: function() {}
    }
    $(document).on('pagechange', function (e, ui) {

        //I redefine customFunction to do what I need, again, you could pass pageDisplayedObj explicitly
        pageDisplayedObj.customFunction = function(ui) {
                console.log("I'm doing something awesome with the ui!");
        };
        $(document).trigger(PAGE_DISPLAYED, pageDisplayedObj);

    });

    $(document).on('pagechange', function (e, ui) {

        //here I'll use the switch
        pageDisplayedObj.customFunction = undefined;
        $(document).trigger(PAGE_DISPLAYED, pageDisplayedObj);

    });
})();