My issue is similar to the one here: paper-menu-button's dropdown (paper-menu) not overlaying other iron-list items, but no adequate solution is proposed there.
The problem is that I have a <paper-dropdown-menu>, which opens up correctly inside the <iron-list> item it is in, but goes underneath the following <iron-list> items: 
I have a simple <paper-dropdown-menu> like this:
<paper-dropdown-menu-light class="custom" label="Languages" no-label-float>
<paper-listbox class="dropdown-content" selected="1">
<paper-item>Spanish</paper-item>
<paper-item>English</paper-item>
<paper-item>French</paper-item>
<paper-item>Sinhala</paper-item>
</paper-listbox>
</paper-dropdown-menu-light>
which is inserted into another element with an <iron-list> (which loads a JSON file with <iron-ajax>):
<iron-list id="list" items="[[bookList.books]]" as="item">
<template>
<div>
<div class$="[[getClassForItem(item, selected)]]" tabindex$="[[tabIndex]]" style="z-index: 1;">
<div class="avatar">[[item.id]]</div>
<div class="pad">
<div class="primary">[[item.titleen]]</div>
<div class="shortText">[[item.slug]]</div>
<div class="longText">[[item.blurb]]</div>
<div class="languagedrop">
<language-drop></language-drop>
</div>
</div>
</div>
</div>
</template>
</iron-list>
I tried setting the z-index for each <iron-list> item to 1, but that did not work. I tried working with <iron-overlay>, but I did not manage to get that done. I'm very new to Polymer, so if anybody has a solution or workaround that would be great.