You could create an archive filesystem, that on the server would be one file. Within that file, it would be a filesystem and be able to store files in it. Depends on how they would be counting how many files you have on the server, and whether or not they would add up too.
To create a filesystem in a filesystem, you could do this for a 10MB filesystem:
> dd if=/dev/zero of=/path/to/filesystem/newfilesys bs=1024 count=10000
> mkfs.ext3 /path/to/filesystem/newfilesys
This will give you a warning, usually, that it is not a block special device. You can continue. Then you would mount the filesystem as you would any other. Problem is that once you mount it, then files added could be added to the total file count!
You could try to upgrade to a larger number of total files on the server, or figure out an archive server to use.