codice:
<!DOCTYPE html><html>
<head>

<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
    $("button").click(function(){
        $("#mioDIV").toggleClass("redBG");
    });
});
</script>


<style type="text/css">
#mioDIV { width:100px; height:100px; }
.greenBG { background:green; }
.redBG { background:red; }
/* IMORTANTE! la classe redBG va definita DOPO greenBG */
</style>

</head>


<body>


<div id="mioDIV" class="greenBG"></div>
<button>Toggle class for element</button>


</body>
</html>