You can if ya really want to. You'd have to sign on with companies that would allow it though. It's worked for some people, others not so well.
As for getting ya more freight. I'd say in my case that no, it didn't. As was mentioned, ya might drive the rates down too. For instance, you're the only truck in BFE. Two companies think they've got a truck there. So when a load comes up they bid against each other, when actually you're the only one there.
Also it's important to communicate to both companies. Some companies will say it's ok to work for 2 but then get upset when ya take a run for the other one. One company that allows ya to work for others will call ya early in the morning every morning to see where you're at. This would be a PITA I guess if ya only worked for only them though. Another company that allows ya to work for others takes quite awhile to pay, like up to 2-3 months. They tell ya that going in, so no one's misleading ya or anything. Still it means you've got to be able to have enough $$ to last that long out there until ya get those first few checks. Basically, the companies that will allow ya to work for others tend to have some drawbacks.
Overall, I guess it can work out. It has for some, so it can be done. My 2 cents likes just dealing w/ one company though.