Actually you can if the companies will allow it. I'm doing just that, albeit w/ not so great results. 2 companies, 0 runs in 2 weeks. In full disclosure I was out of service for 3 days & did have 1 run offer, but couldn't take it. Still, not a lot of work between the 2 companies. Maybe that's why they're fine w/ signing on w/ someone else. They know it's slow. I'll try this setup for another month or so & see if it picks up any. If not I'll re-evaluate things & see what my options are.
So you can sign on w/ more than 1 company. As far as I know you just have to have your own insurance. This costs a bit more than just having bobtail. If ya get 1 run a month from company number 2, it should pay for itself though. Obviously your main company has to allow it too, but it can be done.
If you're going to do this make sure you let company B know if company A gives you a run.