Generally, I'd stay away from changing a person's email. If that person receives important information and their communication is critical to the business, changing an email address can be very troublesome and problematic.
So if we're not changing the email addresses, there are a couple options with different price points:
- Increase the memory in the server. This is perhaps the cheapest method, and probably the easiest too. For less than a few hundred dollars you should be able to at least double the memory on the system.
- Move the spam filter/email server to a different machine. If your webserver gets significant traffic and is critical to your business, it should be on it's own machine, not sharing resources with other services. In the spirit of "you have to spend money to make money", your company should understand that investment in the money-making parts of your technology, at the very least, should be a bit of a priority. It doesn't have to cost a lot. It should just be by itself and cared for as a valuable entity in your business.
- Invest in a gateway filtering solution. Either sign up for a hosted email service that handles all your spam for you, or get an appliance (like Barracuda or similar) that'll do it for you on-site. The hosted solution will probably be cheaper if you're a small organization.
All these suggestions are moot, though, if the account receiving the extreme levels of spam is for the janitor. If this person's outside communication is not critical to the functioning of the business, they can be issued a new email address relatively easily.
I knew I forgot something in this answer. Thanks Aaron for reminding me.
If you give the user a new email address, it is critical that you include training and education in your deployment process. Work email is not to be used as personal email. Gmail, Yahoo, Hotmail, and a plethora of others all offer personal email accounts for free with few limitations or requirements. If the user feels they can sign up for deals and specials and mailing lists using their work account, they need to be informed this is not OK behavior. In fact, using this example of how their poor decisions, even in something as seemingly innocuous as using their work email account to sign up for email lists, cost their company real money and resources, can be a very good teaching tool.
After all, it would really suck to be fired because your email account crashed the mail server which brought down the company website which lost the company critical and profitable business, all because you used your work email to sign up for 300 Cute Kitten Pix listservs. Even I'm having trouble seeing how I'd phrase that on my CV.