Esto te serviría? Código PHP:
<html>
<head>
<title>Untitled</title>
<script>
maximo=6; //Pon aquí el máximo de seleccionables
total=0;
function sumar(esto){
if (esto.checked){
if(total>=maximo){return false}
total+=1;
}
else{total-=1;}
}
</script>
</head>
<body>
<form>
<input type="checkbox" name="cosa" value="aa1" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa1" value="aa2" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa2" value="aa3" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa3" value="aa4" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa4" value="aa5" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa5" value="aa6" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa6" value="aa7" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa7" value="aa8" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa8" value="aa9" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa9" value="aaa" onClick="return sumar(this)">Una cosita<br>
<input type="checkbox" name="cosa10" value="aab" onClick="return sumar(this)">Una cosita<br>
</form>
</body>
</html>