Thank you Juri for your help on this.

I have tested the attached patch (isearch-5.patch)
with `multi-isearch-buffers'/`multi-isearch-files': it seems
OK now.

< To avoid the need to add multi-isearch-end to isearch-mode-end-hook,
< you could try to restore saved variables before calling isearch-mode.
< Then multi-isearch-setup called from isearch-mode should take care of
< adding multi-isearch-end to isearch-mode-end-hook when necessary
< variables are already restored, i.e. when you save the variable
< multi-isearch-next-buffer-function instead of
< multi-isearch-next-buffer-current-function.
I got the point. Actually I bind multi-isearch-next-buffer-function
to multi-isearch-next-buffer-current-function, because the former was nil
and multi-isearch-setup makes a non-nil test for this variable at the
beginning


< multi-isearch-current-buffer still needs to be restored after
< isearch-mode in the same place where you already added it in your patch.
OK.