In Texas a loan officer (originator) must be licensed through and can only represent one broker at a time. Here your current broker must notify the TDSML and surrender the originators license. Then the new broker must sponsor you. a small fee is charged to reissue the LO license in the new brokers name. This is according to the licensing authority in Texas, the Texas Department of Savings and Mortgage Lending, or TDSML.

That all depends on the state you work in and what the licensing laws allow.  For instance, the laws in both Nevada and Utah do not allow you to originate for more than one broker/entity.  You must register your company affiliation with the state regulatory authority and must update your information if you change companies.  Both Utah and Nevada also distinguish between branch locations and if you move from one branch to another, you must report it.

I think you will find this to be the case in almost all 50 states now as most states have imposed tighter control over the mortgage industry.

Unlike many other States, Colorado doesn't prohibit a mortgage professional from working for more than one employer at a time. However, the law does specifically prohibit "...representing a mortgage company other than the licensee's employer without the express knowledge and consent of the employer." www.dora.state.co.us

New York also clearly states that a mortgage broker cannot work for more than one mortgage company at a time. www.banking.state.ny.us

You can find the mortgage lending guidelines in your state by googling "the state" followed by "mortgage lending guidelines"  ex. Colorado Mortgage Lending Guidelines