Bu iş görür sanırım.

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>Live Deneme</title>
    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js"></script>
    <script>
         
    $(document).ready(function(){
        
        $("body").delegate('button', "click", function(){
            
            $(this).after('<button>Daha da tıkla</button>');
             
        });
         
    });
     
    </script>
</head>
<body>
    <button>Tıkla</button>
</body>
</html>