(defun prot/copy-file-to-destinations--directory-prompt ()
  "Produce the directory/destinations prompt of `prot/copy-file-to-destinations'."
  (let ((skip-initial t)
        destinations)
    (while (or skip-initial (y-or-n-p "Add more destinations? "))
      (when skip-initial
        (setq skip-initial nil))
      (push (read-directory-name "Select destination directory: ") destinations))
    destinations))

(defun prot/copy-file-to-destinations (file destinations)
  "Copy FILE to DESTINATIONS.
FILE is a string pointing to a file system path.  DESTINATIONS is a list
of strings representing directories.
‑
In interactive use, prompt for FILE and then for DESTINATIONS.  For each
selected destination, produce a `y-or-n-p' prompt on whether to add
another destination or perform the operation with the selected ones."
  (interactive
   (list
    (read-file-name "File to copy: ")
    (prot/copy-file-to-destinations--directory-prompt)))
  (dolist (destination destinations)
    (copy-file file destination :overwrite-if-it-exists))
  (message "Copied %s to %s" file (mapconcat #'identity destinations ", ")))