Well, if you just explain that to a sysadmin, they're going to (a) explain how they can't give you, a mere user, admin rights, and (b) talk to you for hours about how one guy with admin rights screwed things up and it took them days to fix it...
BUT.
You, or at least the administrator, *can* tell IE (and Windows, in general) to store things in different places. I used to have a Windows box set up where Windows and Program Files were on one drive, and Documents and Settings were on another, so that I'd have one drive I could back up less frequently. I also brought the Start Menu, My Documents, IE's cache, and some other things up to the root level directory so I could get to them more quickly.
Some things break (a lot of software has "C
rogram Files" hard coded), but most things worked fine. So maybe your administrator is willing to do that? Or maybe you can even do it yourself in the registry, if you know how? I no longer remember all the settings, and don't know what rights you need to edit the registry in the first place...