  While Efimov physics in ultracold atoms is usually modeled with an isolated
Feshbach resonance many real world resonances appear in close vicinity to each
other and are therefore overlapping. Here we derive a realistic model based on
the mutual coupling of an open channel and two closed molecular channels while
neglecting short-range physics as permitted by the narrow character of the
considered resonances. The model is applied to three distinct scenarios with
experimental relevance. We show that the effect of overlapping resonances is
manifested most strikingly at a narrow resonance in whose vicinity there is a
slightly narrower one. In this system the Efimov ground state extends not only
over the scattering length zero crossing between the two resonances but also
over the pole of the second resonance to finally meet the dissociation
threshold below it. In the opposite scenario, when a narrow resonance is
considered in the vicinity of a slightly broader one, we observe that the
Efimov features are pushed to lower binding energies and smaller scattering
lengths by a significant factor facilitating their experimental investigation.
Both scenarios are referenced to the case of two narrow resonances which are
far enough away from each other to be effectively decoupled. In this case the
two-channel model results are recovered. Finally, we analyze the rich
excitation spectrum of the system and construct and explain its nodal pattern.
