The better option would be to write your css statement as a class instead of as an ID, unless you're having problems with specificity. If it has to be an ID, remember that IDs should be unique, so you should copy your definition and just give it a new id.
As a good html rule, always try and code in the lowest specificity possible to achieve the effect you want, it will help keep your html maintainable.
I needed this question because of I have a hierarchal menu list script maintained by jQuery for hide and display menu's elements in a PHP script. However, in some pages of the script, I have to deal with two menus. The menu skeleton is included in div with id = treeList, so selecting elements with the same id value should halt jQuery selecting, so I needed to dynamically change the id value with some suffix and then by some way set its css to be equaled to the #treeList set in the CSS file.
However, I followed the approach of adding class attribute to the the div id #treeList and instead of selecting the div with the id alone I selected it using both id and class name, while class name is dynamically generated by the PHP as follows:
<?php $suffix = rand(1,1000); ?>
$('#treeList.<?php echo 'c'.$suffix;?>');
<div id="treeList" class="<?php echo 'c'.$suffix;?>">