Of course you can! Typically doctors work out of several hospitals without owning any of them. If you choose to be a primary care physician you do not need to work out of a hospital at all, you only need an office. You may own your own office or join a group of doctors and own the space together, joining a group helps reduce cost and lets you divide up the duties that go along with owning your own office. If you choose to be a surgeon of some sort where you need to operate out of a hospital typically you would be part of a group that owns office space where you actually see patients. You would then be what they called credentialled with one or more hospitals where you would take your patients for surgery. You do not pay to use the hospital, the hospital collects fees from your patients for their surgery just like you would.
Karyn recommends the following next steps:
As a medical doctor you start building skills during your training; by the time you are practicing independently you can decide what field to choose. Or stay in general health care. There are as many choices to make as there are people on this earth,
I hope this helps you on your way.
You can work in a private hospital as a consulting provider or as an employee of the hospital.
You could even work in an academic setting as a university employee, teaching future doctors.