Yes you can rent what's called a shared environment and overpopulate the server, assuming your clients don't mind a horrible loading speed and they're not getting any real traffic. If they start getting decent traffic, they'll quickly outgrow the environment you're providing for them and their site speed will suffer greatly (to the point of unusable if they happen to get a viral hit and start getting tons of traffic). Every single customer you have would be affected. One of your customers piss somebody off and is getting DDoS'd to bring down their site? Well now it's affecting all of your clients and none of them can access their site. There's many reasons even small start-ups don't want to use shared hosting for their site.
