Passing multiple parameters to the Element API
You can fetch GET parameters using HttpRequestService::getQuery() or getRequiredQuery():

'entries-by-category' =&gt; function() {
    $categoryIds = craft()-&gt;request-&gt;getRequiredQuery('categoryIds');

    return [
        'elementType' =&gt; 'Entry',
        'criteria' =&gt; [
            'relatedTo' =&gt; ['targetElement' =&gt; $categoryIds],
        ],
        // ...
    ];
},