Can you specify a "data-target" for Bootstrap which refers to a sibling DOM element without using an ID?

While it is true that the selector in a data-target attribute is a jQuery selector, the data-api specification for this plugin provides no means of referencing back to this in the scope of execution (see lines 147-153 in bootstrap-collapse.js for its use).

However, I would like to offer another alternative approach, which is to extend the data-api with your own custom toggle specifier. Let's call it collapse-next.

JS ^{(see update note)}

$('body').on('click.collapse-next.data-api', '[data-toggle=collapse-next]', function (e) {
  var $target = $(this).parent().next()
  $target.data('collapse') ? $target.collapse('toggle') : $target.collapse()
})

HTML

<a class="accordion-toggle" data-toggle="collapse-next">

JSFiddle (updated)

Downside here is that it's a rather tightly coupled approach, since the JS presumes a specific structure to the markup.

---

Note about IE issues

As @slhck pointed out in his answer, IE9 and under apparently fail on the first click when using an earlier revision of my answer. The cause is actually not an IE issue at all, but rather a Bootstrap one. If one invokes .collapse('toggle') on a target whose Carousel object is uninitialized, the toggle() method will be called twice - once during initialization and then again explicitly after initialization. This is definitely a Bootstrap bug and hopefully will get fixed. The only reason it doesn't appear as a problem in Chrome, FF, IE10, etc, is because they all support CSS transitions, and hence when the second call is made it short-circuits because the first one is still active. The updated workaround above merely avoids the double-call problem by checking for initialization first and handling it differently.

@merv's solution didn't work for me in IE9 and below, since the collapsible state wasn't available unless you clicked at each item once. It did work fine in Firefox and Chrome though. So after two clicks, everything would work.

What I did was set a .collapse-next class to the triggering elements, then force their ul siblings to collapse with toggle set to false:

$(".collapse-next").closest('li').each(function(){
  if ($(this).hasClass('active')) {
    // pop up active menu items
    $(this).children("ul").collapse('show');
  } else {
    // just make it collapsible but don't expand
    $(this).children("ul").collapse({ toggle: false });
  }
});

This is for actually toggling the menu state:

$('.collapse-next').click(function(e){
  e.preventDefault();
  $(this).parent().next().collapse('toggle');
});

It seems that using data- attributes is a somewhat more modern and cleaner approach, but for old browsers working with classes and jQuery seems to do the job as well.

No javascript solution or the solution depends on bootstrap's JS already in use, just exploiting the DOM structure-

See the data-target=""...

A hint to avoid bulky solutions and need no ID or extra JS, trick using markup placement-

<button data-toggle="collapse" data-target=".dropdown-toggle:hover + .more-menu" type="button" class="btn btn-primary dropdown-toggle" >
  Show More Menu +
</button>
<div class="collapse more-menu">More menu here...</div>

This CSS selection structure will select the desired DOM .dropdown-toggle:hover + .more-menu and there we can apply our desired CSS. There are more ways to exploit what we have. :hover or :active or so many other ways.