Can I add an accessory dwelling unit?

Apex calls this an accessory apartment (Sec. 4.5.6), and yes, one is permitted as an accessory use to a principal single-family dwelling in every residential district plus MORR (per the Use Table, Sec. 4.2.2). An apartment attached to the principal home has no size cap. A detached accessory apartment is capped at 40 percent of the principal home's heated square footage outside the Small Town Character Overlay District, or the smaller of 50 percent or 1,000 heated square feet inside that overlay. The accessory apartment must stay in the same ownership as the principal home in residential districts, use similar materials, and meet the detached-accessory-structure dimensional standards of Sec. 5.2.7 if detached. Accessory apartments are also allowed above the ground floor of commercial buildings in B1, B2, B3, MEC-CZ, TND-CZ, PUD-CZ, MORR, and SD-CZ, with separate ownership from the commercial use permitted there. Confirm the district and any overlay for the parcel with Planning and Community Development at 919-249-3426.