What conditions must be met in order to upload .zip file to a multisite WordPress installation?

I cannot upload .zip files to my WordPress network, despite making IMHO everything that is needed. I am still hit by this irritating error.

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Details:

  1. I am a super-admin in my network.
  2. The ALLOW_UNFILTERED_UPLOADS flag is set to true
  3. Custom hook of $ existing_mimes['zip'] = 'application/zip'; is added
  4. Uploading .zip files is allowed in my network:

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Here is entire code of my hook:

function so_387865_custom_upload_mimes ( $  existing_mimes ) {     $  existing_mimes['epub'] = 'application/epub+zip';     $  existing_mimes['mobi'] = 'application/x-mobipocket-ebook';     $  existing_mimes['zip'] = 'application/zip';       return $  existing_mimes; }   add_filter('upload_mimes', 'so_387865_custom_upload_mimes'); 

I thought that maybe there’s something wrong with the hook, so I have installed the Enhanced Media Library extension (as suggested in here). All for nothing, as it clearly shows that this MIME type is added:

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What else should I do in order to be able to upload .zip files? I am seriously lost!