I have a lot of linux systems running in places where I can only access them over SSH, the problem is that I need to write over the system harddrive on those systems to update them. I wonder about the best way to do this?
This Debian-centric howto should be helpful, if not exactly what you need.
I would suggest creating a 2. Partition, install everything chrooted to this Partition and configure Grub to try to boot the new system on startup, I would also configure a Fail over so that Grub only tires to boot the new system the next time, and then again boots the old system if it fails and you reboot again. When everything is running fine configure Grub to boot the new system by default, and you can erease the old one. After all is done you can recombine the Partions if you like, but it might be smart to keep them around just in case you are doing something like this again.