Updated Answer

Trying to open multiple panels of a collapse control that is setup as an accordion i.e. with the data-parent attribute set, can prove quite problematic and buggy (see this question on multiple panels open after programmatically opening a panel)

Instead, the best approach would be to:

1. Allow each panel to toggle individually
2. Then, enforce the accordion behavior manually where appropriate.

To allow each panel to toggle individually, on the data-toggle="collapse" element, set the data-target attribute to the .collapse panel ID selector (instead of setting the data-parent attribute to the parent control. You can read more about this in the question Modify Twitter Bootstrap collapse plugin to keep accordions open.

Roughly, each panel should look like this:

<div class="panel panel-default">   <div class="panel-heading">         <h4 class="panel-title"             data-toggle="collapse"              data-target="#collapseOne">             Collapsible Group Item #1         </h4>    </div>    <div id="collapseOne"          class="panel-collapse collapse">        <div class="panel-body"></div>    </div></div>

To manually enforce the accordion behavior, you can create a handler for the collapse show event which occurs just before any panels are displayed. Use this to ensure any other open panels are closed before the selected one is shown (see this answer to multiple panels open). You'll also only want the code to execute when the panels are active. To do all that, add the following code:

$('#accordion').on('show.bs.collapse', function () {    if (active) $('#accordion .in').collapse('hide');});

Then use show and hide to toggle the visibility of each of the panels and data-toggle to enable and disable the controls.

$('#collapse-init').click(function () {    if (active) {        active = false;        $('.panel-collapse').collapse('show');        $('.panel-title').attr('data-toggle', '');        $(this).text('Enable accordion behavior');    } else {        active = true;        $('.panel-collapse').collapse('hide');        $('.panel-title').attr('data-toggle', 'collapse');        $(this).text('Disable accordion behavior');    }});

Working demo in jsFiddle

For whatever reason $('.panel-collapse').collapse({'toggle': true, 'parent': '#accordion'}); only seems to work the first time and it only works to expand the collapsible. (I tried to start with a expanded collapsible and it wouldn't collapse.)

It could just be something that runs once the first time you initialize collapse with those parameters.

You will have more luck using the show and hide methods.

Here is an example:

$(function() {  var $active = true;  $('.panel-title > a').click(function(e) {    e.preventDefault();  });  $('.collapse-init').on('click', function() {    if(!$active) {      $active = true;      $('.panel-title > a').attr('data-toggle', 'collapse');      $('.panel-collapse').collapse('hide');      $(this).html('Click to disable accordion behavior');    } else {      $active = false;      $('.panel-collapse').collapse('show');      $('.panel-title > a').attr('data-toggle','');      $(this).html('Click to enable accordion behavior');    }  });});

http://bootply.com/98201

Update

Granted KyleMit seems to have a way better handle on this then me. I'm impressed with his answer and understanding.

I don't understand what's going on or why the show seemed to be toggling in some places.

But After messing around for a while.. Finally came with the following solution:

$(function() {  var transition = false;  var $active = true;  $('.panel-title > a').click(function(e) {    e.preventDefault();  });  $('#accordion').on('show.bs.collapse',function(){    if($active){        $('#accordion .in').collapse('hide');    }  });  $('#accordion').on('hidden.bs.collapse',function(){    if(transition){        transition = false;        $('.panel-collapse').collapse('show');    }  });  $('.collapse-init').on('click', function() {    $('.collapse-init').prop('disabled','true');    if(!$active) {      $active = true;      $('.panel-title > a').attr('data-toggle', 'collapse');      $('.panel-collapse').collapse('hide');      $(this).html('Click to disable accordion behavior');    } else {      $active = false;      if($('.panel-collapse.in').length){        transition = true;        $('.panel-collapse.in').collapse('hide');             }      else{        $('.panel-collapse').collapse('show');      }      $('.panel-title > a').attr('data-toggle','');      $(this).html('Click to enable accordion behavior');    }    setTimeout(function(){        $('.collapse-init').prop('disabled','');    },800);  });});

http://bootply.com/98239

To keep the accordion nature intact when wanting to also use 'hide' and 'show' functions like .collapse( 'hide' ), you must initialize the collapsible panels with the parent property set in the object with toggle: false before making any calls to 'hide' or 'show'

// initialize collapsible panels$('#accordion .collapse').collapse({  toggle: false,  parent: '#accordion'});// show panel one (will collapse others in accordion)$( '#collapseOne' ).collapse( 'show' );// show panel two (will collapse others in accordion)$( '#collapseTwo' ).collapse( 'show' );// hide panel two (will not collapse/expand others in accordion)$( '#collapseTwo' ).collapse( 'hide' );