If you oversell, then when customers start to use all the resources they've paid for, you can
SHORT TERM FIXES
* purchase extras from your provider (if it's bandwidth)
* ditch archived system files / backups / log files if it's disk space they need
While you're breathing a quick sigh of relief, you then get another server and start looking for clients who would be amenable to moving to a new server.
I will warn you, though, as someone who's been with hosts when this happens: your credibility takes a huge nosedive. It's annoying, it's inconvenient, it's a big fat hassle, and as a customer you start wondering what else your hosting provider is shorting on.
In any business, you should never let yourself get so close to the wall that it can reach out and smite you. It's just a bad idea. Whether it's having enough inventory on hand, or enough personnel on the regular staff to handle peak service times, or knowing where to get additional personnel / inventory in a hurry - a business had best be able to quickly take care of its clients. It can be oh so tempting to cut corners (believe me, I know - I'm there right now on another issue), but in you always have to look seriously at what concessions you'll need to make if / when things start getting busier. Sometimes, you'll come to the conclusion that you can skimp on something in one or two cases because the solution is rather painless. Often, though, it's not worth the initial or shorter-term savings.