I run a commercial warehouse building in New York City.
There is a sole tenant that rents the entire 9 story building.
That tenant is responsible for maintaining the 3 freight elevators.
The tenant has a maintenance contract with a licensed elevator contractor.
There are violations on the elevators because the tenant is in arrears to the elevator contractor.
The owners of the building want to get the violations off the books so they are getting their own different elevator contractor to do the work.
My question is- If there is already an elevator contractor with a maintenance contract on the elevators who is owed money for maintenance, can a second contractor come in and do work on those elevators?

Ay-Caramba, Elevator Company's do like to be paid for services rendered. As do we all. However if there are safety violations and you as the owner feel an obligation to the using public for a safely operating Elevator, you can contact the Elevator company in question and see if they will Contract with you to do the work. If they refuse you should Contract with another Company. I would be up front with the other company and explain the situation. In all probability they will be happy for the work.

John Jay is giving you great advice. It's the fair thing to do.

The company that has maintained your elevator has his skin in the game. If the tenant is having difficulty paying his bills you can't blame the contractor for discontinuing his service until the open balance is paid.

As an owner, I struggle with this every day!

Unless you have an inspection only or oil and grease only contract the elevator company that has been hired to do maintenance is usually responsible for preventing basic defiance's like dirty car tops, pit, machine room, emergency lighting, bells, house keeping etc.. You should not have to hire another company to do work that the first company should be responsible for. If they refuse to take care of these issues you need to read the fine print in your contract. If you do not know when kind of wording you need to represent you in an elevator maintenance contract you should hire an elevator consultant to help you.

Maintenance contracts vary widely and often include language that precludes you having anyone else work on the equipment during the contract's term. Also, having another company work on the equipment gives both the visiting provider and your routine maintenance provider an opening to "scarecrow", each blaming the other, then charge you for any and all future problems. If you aren't having independent assessment, you have lttle means of regulating.