A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir R as consisting of a large collection of elementary ancillas: the dynamics of the open system S results from successive "collisions" of S with the ancillas of R. Here, we present a general formulation of memoryless composite CMs, where S is partitioned into the very open system under study S coupled to one or more auxiliary systems {S_i}. Their composite dynamics occurs

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... ough internal S-{S_i} collisions interspersed with external ones involving {S_i} and the reservoir R. We show that important known instances of quantum non-Markovian dynamics of S -- such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise -- can be mapped on to such memoryless composite CMs.