High penetrations of distributed energy resources (DERs) are driving the transformation of traditional distribution networks into transactive energy distribution systems (TEDS). TEDS depart from conventional distribution system constructs to 1) enable a local distribution operator to maximize social welfare, 2) enable peer-to-peer energy transactions, 3) extract maximum participation and benefits from DERs, 4) usher in competition in the distribution sector to supply electricity via DERs, and 5) hold the potential for a lower asset cost solution, greater customer choice, and higher reliability. The conventional distribution system planning is inadequate for this purpose. Following the new TEDS paradigm, an incremental capacity auction (ICA) is proposed in this paper considering: 1) bids for power capacity from all energy sources (DERs and transmission), 2) bids for network asset upgrades from equipment vendors, and 3) bids from new loads. A holistic auction settlement procedure is developed for the proposed ICA mechanism that can concurrently determine the optimal power capacity to be procured and network asset upgrading, while maximizing social welfare. Further, locational marginal price for power capacity demand is estimated as a by-product of the ICA solution. Benefits are demonstrated via case studies and include increased participation of DERs to supply energy, maximizing the social welfare, and enabling assets deferral considering the available local resources.