some techniques you could use:

Consider controlling your network jacks, only enable ones that your employees need, that prevents someone from plugging into a spare jack and gaining access to the network.

Now, the problem here is that someone can unplug one of your machines and plug theirs in, so then you need to use MAC filtering. This is a pain in the butt, but I have seen one (large) financial instituion doing this with some success.

These two technical fixes can most likely be done with your existing equipment so the cost shouldn`t be too high.

To protect your workstations ensure that all emloyees are using password protected screensavers and enable them when they are away from there desk. Also ensure strong passwords are enforced (nothing thats easily crackable). To do this successfully you are going to need to look at a security awareness program which makes your employees aware of the risks (this should be generic, not just against this one company!) otherwise people will write passwords on post-its, choose their dogs name, etc... Also a security awareness program can be cheap to implement and have a high return on investment (good to mention to your VP). As you are going to be sharing office space I think making your users aware of information security risks must be the number one priority.

Also be aware of the risk that someone could steal your equipment, so asset tags, hardware locks etc...could all be useful investments, but all cost.

Also make sure your offices have decent locks on the doors and that office are locked after hours (unless someone is in them).

Hope this helps.