It depends on the area you are in, but typically there are many non oem 3rd party company's in the larger markets.

I would highly advise that you make sure the company you hire has the full capability to maintain the elevator you have. Often the newer elevators require special diagnostic tools that 3rd party company company's do not have access to. I have seen comapnys charge for maintenance for years and then one day the elevator goes down and they have no way to fix it and you have to hire the OEM. I'm not saying this in support of the OEM, just advising you to do your due diligence when picking a new provider.