A monolithic combustor body may provide multi-stage combustion. A combustor body may include a combustion chamber body and a plurality of heating walls that include a heat sink. The combustion chamber body may be disposed annularly about a longitudinal axis and defining a combustion chamber. The plurality of heating walls may include heat sink. The plurality of heating walls may occupy a radially or concentrically outward position relative to the combustion chamber and may define a corresponding plurality of combustion-gas pathways fluidly communicating with at least a proximal portion of the combustion chamber. During operation, the combustor body may exhibit multi-stage combustion that includes a first combustion zone occupying a distal or medial position of the combustion chamber relative to the longitudinal axis, and a second combustion zone occupying a proximal position relative to the first combustion zone and a radially or concentrically outward position of the combustion chamber and/or a radially or concentrically inward position of the plurality of combustion-gas pathways.