Hi Adam,
Extremely sorry for the late reply. I saw your post but missed to reply.
If you have only one multiline parameter then you can use “enclosed content” parameter.
So what you can do is, insert the parameter $$enclosed_content$$
in shortcode content. Now while using the shortcode you can do like below,
[sc name="my_shortcode"]
<ul>
<li>Multiple</li>
<li>Lines</li>
</ul>
[/sc]
Note that here the parameter is not passed via attributes instead within [sc][/sc]
Thanks
Aakash