A distinguishing feature of ultracold collisions of bosonic lithium atoms is the presence of two neardegenerate two-body continua. The influence of such a near-degeneracy on the few-body physics in the vicinity of a narrow Feshbach resonance is investigated within the framework of a minimal model with two atomic continua and one closed molecular channel. The model allows analysis of the spin composition of loosely bound dimers and trimers. In the two-body sector the wellestablished coupled-channels calculations phenomenology of lithium is qualitatively reproduced, and its particularities are emphasized and clarified. In the three-body sector we find that the Efimov trimer energy levels follow a different functional form as compared to a single continuum scenario while the thresholds remain untouched. This three-channel model with two atomic continua complements our earlier developed three-channel model with two molecular channels [1] and suggests that the experimentally observed exotic behavior of the first excited Efimov energy level [2] is most probably caused by the short-range details of the interaction potential.