Memories are thought to be stored in neural ensembles known as engrams that are specifically reactivated during memory recall. Recent studies have found that memory engrams of two events that happened close in time tend to overlap in the hippocampus and the amygdala, and these overlaps have been shown to support memory linking. It has been hypothesized that engram overlaps arise from the mechanisms that regulate memory allocation itself, involving neural excitability, but the exact process remains unclear. Indeed, most theoretical studies focus on synaptic plasticity and little is known about the role of intrinsic plasticity, which could be mediated by neural excitability and serve as a complementary mechanism for forming memory engrams. Here, we developed a rate-based recurrent neural network that includes both synaptic plasticity and neural excitability. We obtained structural and functional overlap of memory engrams for contexts that are presented close in time, consistent with experimental and computational studies. We then investigated the role of excitability in memory allocation at the network level and unveiled competitive mechanisms driven by inhibition. This work suggests mechanisms underlying the role of intrinsic excitability in memory allocation and linking, and yields predictions regarding the formation and the overlap of memory engrams.