I'am not aware of any DOT regulation that say's you cannot be leased to more than one company at a time. However the carriers you are considering leasing to will probably not allow you to have multiple lease's, due to liability. Get a lawyer to review any lease's.
With your own authority, Basic bobtail,Physical damage,& cargo will run around 9K a year if you have a good driving record, OOIDA can do it all and they are reasonable ( reefer insurance is higher $$$$ )
Please do not take this the wrong way but you have asked a few very basic questions about trucks & trucking. I would suggest you take a look at the web site
www.writeuptheroad.com Tim Brady has a good selection of books and info to help you gain more knowledge of the trucking business.
Keep asking questions;You are on the right track