Augmenting responses (AR) are characteristic recruitment phenomena that can be generated in target neural populations by repetitive intracortical or thalamic stimulation and that may facilitate activity transmission from thalamic nuclei to the cortex or between cortical areas. Experimental evidence suggests a role for cortical layer 5 in initiating at least one form of augmentation. We present a three-compartment model of tufted layer 5 cells (TL5) which faithfully reproduces a wide range of dynamics in these neurons that previously has been achieved only partially and in much more complex models. Using this model, the simplest network exhibiting AR was a single pair of TL5 and inhibitory (IN5) neurons. Intracellularly, AR initiation was controlled by low-threshold Ca²⁺ current (I_T) which promoted TL5 rebound-firing, while AR strength was dictated by inward-rectifying current (I_h) which regulated TL5 multiple-spike firing and also prevented excessive firing under high-amplitude stimuli. Synaptically, AR was significantly more salient under concurrent stimulus delivery to superficial and deep dendritic zones of TL5 cell than under conventional single-zone stimuli. Moreover, slow GABA_B -mediated inhibition in TL5 cells controlled AR strength and frequency range. Finally, a network model of two cortical populations interacting across functional hierarchy showed that intracortical AR occurred prominently upon exciting superficial cortical layers either directly or via intrinsic connections, with AR frequency dictated by connection strength and background activity. Overall, the investigation supports a central role for TL5-IN5 skeleton network in low-frequency cortical dynamics in vivo, particularly across functional hierarchies, and presents neuronal models that facilitate accurate large-scale simulations.