Which Rating System?

our company was just brought in on a building that is looking to get LEED certified. They are renovating the building by floors so it is an on-going project that will not be completed for about 5-6 years. The building is still in use while these renovations are taking place. Each floor that has been renovated has been designed to LEED standards. The owner wants the whole building to be certified as soon as possible in order to rent out the spaces (it is a commercial building). Is it possible to go for LEED EBOM now while the renovation is going on and then certify the whole building under NC when it is complete? What is the best way to go about this? Should we get each floor certified or get the whole building certified when all of the renovation is complete? Also, if we are to get the whole building certified, how do we go about collectively combining this information for each floor? Which rating system would work best for this project?