Media manager multiple selection

I’ve edited your code a little and the alert() runs for each selected item. Note that in your code you execute a return too early that make the code bellow don’t run after the first run. Also, you use the same name for a function and for a string var, which is not very appropiate.

function get_the_extension(url) {
    var ext=(url = url.substr(1 + url.lastIndexOf("https://wordpress.stackexchange.com/")).split('?')[0]).substr(url.lastIndexOf("."));
    return ext;
}

jQuery(document).ready(function($){

    var custom_uploader;
    $('#songbook_addfile_button').click(function(e) {
        e.preventDefault();
        //If the uploader object has already been created, reopen the dialog
        if (custom_uploader) {
            custom_uploader.open();
        }
        //Extend the wp.media object
        custom_uploader = wp.media.frames.file_frame = wp.media({
            title:"blemblem",
            button: {
                text:"blemblem"
            },
            multiple: true
        });
        custom_uploader.on('select', function() {
            var selection = custom_uploader.state().get('selection');
            selection.map( function( attachment ) {
                attachment = attachment.toJSON();
                var the_extension = get_the_extension(attachment.url).replace('.','');
                    alert(the_extension);
                    //...one commented line, that was to add files into HTML structure - works     perfect, but only once
            });
        });
        custom_uploader.open();
    });
});