I haven’t tested this out, but I think how this would work is that you could pass an argument to comments_template() which is a file that doesn’t exist, i.e. comments_template( 'custom-comments' ). Since that doesn’t exist, Acorn will load resources/views/partials/comments.blade.php which will then be included by comments_template(). Since it’s included, you should then have access to the $file variable (in this case containing 'custom-comments') in your comments.blade.php partial, and you could use a switch or similar to then load an appropriate other file.
Keep in mind I only woke up like an hour ago, though. I might be over-complicating this.