function addClass(id,new_class){

       var i,n=0;

       new_class=new_class.split(",");

       for(i=0;i<new_class.length;i++){

               if((" "+document.getElementById(id).className+" ").indexOf(" "+new_class[i]+" ")==-1){

                       document.getElementById(id).className+=" "+new_class[i];

                       n++;

               }

       }

       return n;

}

<div id="changeme" class="big red"></div>

<button onclick="addClass('changeme', 'round')">Add a class</button>