One truck leased, one truck under my authority?

I currently have a truck leased on to a carrier. I recently bought another truck. The new truck is going to be set up for a local opportunity.
My question is: can I leave the first truck under lease and run the new truck under my own authority?

 

My thought was the insurance company would have the ultimate say. Don't really want to carry liability and cargo on the leased truck

 

Do they also have trucks under their own authority? Say they own 4 trucks: 2 leased to abc, 1 leased to xyz, and 1 on their own MC#

 

The leased truck has plates provided by the operating carrier. I only carry "non-trucking" insurance on it.

 

I guess what makes this a difficult question is: the leased truck will be parked when the local truck is running. I will be the driver for both trucks. The local thing is seasonal (grain hopper)