Of course, you can create a /work partition. A better wording, however, would be that you can create a /work directory, and mount a partition to it.
Making directories outside your home directory requires you to act as the root user. In Ubuntu, one can execute a command with root priviledges by preceding it with sudo. Thus
sudo mkdir /work
will create a directory work at the top level (/) of the directory structure.
Then you can mount a partition to that directory. That involves editing /etc/fstab. It is described in many places, including on this site. Alternatively, you can use the utility "Disks" to set up a partition to mount automatically during startup in a directory you choose (/work) in this case.
Once you mount that partition there, you want to learn about linux permissions and symbolic links. On the partition, you can create folders, which you then could give to the different users on your system. With symlinks, you can make these folders directly accessible from within the user's home directory, i.e., preventing the need for your users to navigate out of their own home directory.
