  Soft spheres interacting via a hard core and range of attractive and
repulsive "soft-shoulder" potentials self-assemble into clusters forming a
variety of mesophases. We combine a mean field theory developed from a lattice
model with a level surface analysis of the periodic structures of soft-sphere
aggregates to study stable morphologies for all clustering potentials. We
develop a systematic approach to the thermodynamics of mesophase assembly in
the low-temperature, strong-segregation and predict a generic sequence of
phases including lamella, hexagonal-columnar and body-center cubic phases, as
well as the associated inverse structures. We discuss the finite-temperature
corrections to strong segregation theory in terms of Sommerfeld-like expansion
and how these corrections affect the thermodynamic stability of bicontinuous
mesophase structures, such as gyroid. Finally, we explore the opposite limit of
weakly-segregated particles, and predict the generic stability of a
bicontinuous cluster morphology within the mean-field phase diagram.
