<div class="demo">
    <p>Available Boxes (click to select multiple boxes)</p>
    <ul id="draggable">
        <li>Box #1</li>
        <li>Box #2</li>
        <li>Box #3</li>
        <li>Box #4</li>
    </ul>

    <p>My Boxes</p>
    <ul id="droppable">
    </ul>

</div>

$(document).ready(function(){

    var selectedClass = 'ui-state-highlight',
        clickDelay = 600,     // click time (milliseconds)
        lastClick, diffClick; // timestamps

    $("#draggable li")
        // Script to deferentiate a click from a mousedown for drag event
        .bind('mousedown mouseup', function(e){
            if (e.type=="mousedown") {
                lastClick = e.timeStamp; // get mousedown time
            } else {
                diffClick = e.timeStamp - lastClick;
                if ( diffClick < clickDelay ) {
                    // add selected class to group draggable objects
                    $(this).toggleClass(selectedClass);
                }
            }
        })
        .draggable({
            revertDuration: 10, // grouped items animate separately, so leave this number low
            containment: '.demo',
            start: function(e, ui) {
                ui.helper.addClass(selectedClass);
            },
            stop: function(e, ui) {
                // reset group positions
                $('.' + selectedClass).css({ top:0, left:0 });
            },
            drag: function(e, ui) {
                // set selected group position to main dragged object
                // this works because the position is relative to the starting position
                $('.' + selectedClass).css({
                    top : ui.position.top,
                    left: ui.position.left
                });
            }
        });

    $("#droppable, #draggable")
        .sortable()
        .droppable({
            drop: function(e, ui) {
                $('.' + selectedClass)
                 .appendTo($(this))
                 .add(ui.draggable) // ui.draggable is appended by the script, so add it after
                 .removeClass(selectedClass)
                 .css({ top:0, left:0 });
            }
        });

});

<ul>
    <li>One</li>
    <li>Two</li>
    <li>Three</li>
</ul>
<ul>
    <li>Four</li>
    <li>Five</li>
    <li>Six</li>
</ul>

$("ul").on('click', 'li', function (e) {
    if (e.ctrlKey || e.metaKey) {
        $(this).toggleClass("selected");
    } else {
        $(this).addClass("selected").siblings().removeClass('selected');
    }
}).sortable({
    connectWith: "ul",
    delay: 150, //Needed to prevent accidental drag when trying to select
    revert: 0,
    helper: function (e, item) {
        var helper = $('<li/>');
        if (!item.hasClass('selected')) {
            item.addClass('selected').siblings().removeClass('selected');
        }
        var elements = item.parent().children('.selected').clone();
        item.data('multidrag', elements).siblings('.selected').remove();
        return helper.append(elements);
    },
    stop: function (e, info) {
        info.item.after(info.item.data('multidrag')).remove();
    }

});

<style>
    ul {border:1px solid Black;width:200px;height:200px;display:inline-block;vertical-align:top}
    li {background-color:Azure;border-bottom:1px dotted Gray}
    li.selected {background-color:GoldenRod}
</style>
<h1>Click items to select them</h1>
<ul>
    <li>One</li>
    <li>Two<li>
    <li>Three</li>
</ul><ul>
    <li>Four</li>
    <li>Five<li>
    <li>Six</li>
</ul>
<script>
    $("li").click(function(){
        $(this).toggleClass("selected");
    })
    $("ul").sortable({
        connectWith: "ul",
        start:function(e,info){
            // info.item.siblings(".selected").appendTo(info.item);
            info.item.siblings(".selected").not(".ui-sortable-placeholder").appendTo(info.item);

        },
        stop:function(e,info){
            info.item.after(info.item.find("li"))
        }
    })
</script>

$('ul.sortable').multisortable();