Nested add forms of multiple tables via form buttons

Need Help
2

The last option seems most feasible for me, so I want to implement the following form code after clicking a button:

<?= $this->Form->create($product) ?> 
            <?php
                echo $this->Form->control('song_name');
               ...
            ?>
        </fieldset>
        <?= $this->Form->button(__('Submit')) ?>
        <?= $this->Form->end() ?>
    </div>

I did not find a direct way to run code from a button (even though I thought onclick would work as an HTML attribute?), so I implemented like this in the add.php of song request:

echo $this->Form->postButton(‘add new song’, ‘nested_song_form.php’);

with the former code in nested_song_form. However, clicking the button leads to no execution of this code, but staying on the same page with the error that the song request could not be saved.