2 trucks one leased other own authority?

So my question is in the title. I have 2 trucks one Iam driving and it’s leased on to a company. Looking to put a driver in this truck and continue to be leased. Second truck I am wanting to use own authority and dot. Is this possible? I know insurance will want me to cover both trucks but being first truck is leased to company I should be fine right?
Can someone explain please

 

My own

 

So I talked to an insurance company and asked the same question. They said since I have bobtail coverage under my corp for when truck is parked on leased truck. I will have problems down the line they stated I should open another corp to be able to do what I’m asking. I believe they just want to sell me on getting more coverage.

 

Why would it matter though if first truck is leased on. You can’t put two policies on one truck. There’s a lease agreement. As far as second truck being on my irp I don’t see a problem there just don’t see why they would say I would have a problem down the line if I do it like that?!