I think we have a problem with terminology here. To start with, how many different sets of conductors are you getting from the utility? In most cases, you are only allowed to get one "service" into a building from the utility. In what sense are you saying you have six "services"?
Next, once power makes its way into the building, what type of equipment does it connect to? Is it terminated on a switchgear or switchboard? Are there six such switchgear or swichboards? Do they have main breakers?
The six disconnect rule has to do with the ability to turn off all power coming into a building from one location, and to do so with minimal effort. If for example you have one service that is connected to a main switchboard that has a main breaker, then you can turn off all power to the building with one throw of a handle. Within the switchboard itself, then, you can have an unlimited number of breakers serving loads throughout the building. But if the main switchboard did not have a main breaker, then it may have no more than six breakers serving loads in the building, so that you could turn off all power to the building by throwing (at most) six handles.
