Well, if there is an exception for apartments, it is only there to suit the company.
You could share an apartment with one or two other guys, and nobody would really mind. Don't advertise it too much, then you should be okay.
Otherwise: Cheap accommodation in DXB? HAHAHAHAHA!
Be aware that you can not live together with your girlfriend before you get married. They have another law against that, too. I'm mentioning it, because I know a guy who got to be together with one of the CC. They wanted to move together, but she still keeps her company-provided room anyway. So legally, they live separatedly, to avoid any kind of problems.