< file_for_send.sh is attached to the stdin of parallel. Even if this stdin ultimately is inherited by ssh (and I don't know if it is), it's not that each ssh will reopen the file and read it from the beginning. Write a script that takes (at least) user@server as an argument and handles a single case of ssh inside, including the redirection from file_for_send.sh. Then let parallel run the script multiple times. Maybe there is a clever option for parallel to fork (tee-like) its stdin, but I don't know the tool good enough to tell.