(defun mod-hook-text-prop (&rest args)
  (message "mod-hook-text-prop %S, inhibit? %S" args inhibit-modification-hooks))
(defun mod-hook-ov-prop (&rest args)
  (message "mod-hook-ov-prop %S, inhibit? %S" args inhibit-modification-hooks))
(defun mod-hook-change-fun (&rest args)
  (message "mod-hook-change-fun %S, inhibit? %S" args inhibit-modification-hooks))


(with-current-buffer (get-buffer-create "*test*")
  (insert (propertize "foo\n" 'modification-hooks '(mod-hook-text-prop)))
  (let ((ov (make-overlay (point-min) (point-max) )))
    (overlay-put ov 'modification-hooks '(mod-hook-ov-prop)))
  (setq-local before-change-functions '(mod-hook-change-fun))
  (setq-local after-change-functions '(mod-hook-change-fun))
  (goto-char (point-min))
  (delete-char 3)
  (insert "bar"))