Operating on a different state while registered on another

You do not need to submit any paperwork to the FMCSA just to work in a different state, unless you mean that you are going to need your own operating authority. If you are leasing under their authority then there is nothing to submit to the FMCSA or any one else for that matter.

As for your base plate, do you own the Texas plate or does the carrier you are leased to now? Will the new carrier require you to get your own base plate or use theirs? The reason I ask is if the carrier owns it you will have to turn it in to them when you leave and get a new plate for your truck from the new carrier or on your own. If you own it then you will need to either surrender it to Texas and get a New Mexico plate, or if you plan on taking the truck home to Texas then I would get it upgraded to an apportioned plate ( IRP) if it is not already. This will allow you to drive in both Texas and New Mexico along with other states but is more expensive than just an intrastate Texas or New Mexico weight distance plate. If the truck is going to stay in New Mexico and not leave the state then you can get a NM weight distance plate, this is their plate for heavier trucks that are subject to the weight distance tax. You will also have to register with the state of New Mexico and pay the tax for every mile you drive there.

The New Mexico Trucking Association has a great staff and helps a lot of small business truckers with regulatory compliance, visit their website at http://www.nmtrucking.org