Can you buy a portion of a rental building?

My husband and I rent a carriage house that is in the back yard of a small, 4 story 16 unit building. The house is completely detached from the main building, but you must walk through the main hallway to get to the backyard/house area. It's been a dream of ours to buy the carriage house from the property owner, but have no idea if that is even possible. Before I go to the owner, I wanted to get all my facts straight so I can present him with all available options. How would I go about researching this? Should I see a real estate lawyer? Or someone else in the real estate business?