A recent study suggests that the observed multiplicity of super-Earth (SE) systems is correlated with stellar clustering: stars in high phase-space density environments have an excess of single-planet systems compared to stars in low density fields. This correlation is puzzling as stellar clustering is expected to influence mostly the outer part of planetary systems. Here we examine the possibility that stellar flybys indirectly excite the mutual inclinations of initially coplanar SEs, breaking their co-transiting geometry. We propose that flybys excite the inclinations of exterior substellar companions, which then propagate the perturbation to the inner SEs. Using analytical calculations of the secular coupling between SEs and companions, together with numerical simulations of stellar encounters, we estimate the expected number of effective flybys per planetary system that lead to the destruction of the SE co-transiting geometry. Our analytical results can be rescaled easily for various SE and companion properties (masses and semi-major axes) and stellar cluster parameters (density, velocity dispersion and lifetime). We show that for a given SE system, there exists an optimal companion architecture that leads to the maximum number of effective flybys; this results from the trade-off between the flyby cross section and the companions impact on the inner system. Subject to uncertainties in the cluster parameters, we conclude that this mechanism is inefficient if the SE system has a single exterior companion, but may play an important role in SE + two companions systems that were born in dense stellar clusters.
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