ssh is in fact just passing a string to the remote host. There this string is given to a shell which is supposed to interpret it (the user’s login shell, which is typically something like bash). So whatever you want to execute needs to be interpretable by that remote login shell, that’s the whole rule you have to stick to.
You can indeed just use newlines within the command string:
ssh alfe@sweethome "
ls /home/alfe/whatever
ping foreignhost
date
rm foobar
"