For handling the utility interconnects:
All electrical power and communications could be sent through slip rings located in the base. This would just be an AC version of the brushes on a DC motor.
Sewage could also be handled by a slip ring type system. The rotating waste pipes would open onto a circular drain of some type. You'd get an effect similar to Lecom's circular vomit ring.
For potable water, water could pour from a stationary spigot into a rotating circular tank. From there a pump would lift the water to a holding tank on the roof for pressure.
The main drawback is that these slip ring systems will be large and take up a lot of room in the base of the core, and maintainence probably sucks. But they are technically doable.