How to remount /var over ssh

I have a /var directory that sometimes gets too large for the partition it's on. It would be beneficial if I could mount this directory on a larger partition. I don't have physical access to this machine though. Only SSH and similar remote access. How can I remount /var **safely** on a machine that I don't have physical access to? The only solutions I know of involve boot discs or init 1, so the popular directory isn't accessed during the transition.