Shallow cut-and-cover underground structures, such as subway stations, are traditionally designed as rigid boxes (moment-resisting connections between the main structural members), seeking internal hyperstaticity and high lateral (transverse) stiffness to achieve important seismic capacity. However, since seismic ground motions impose racking drifts, this proved rather prejudicial, with great structural damage and little resilience. Therefore, two previous papers proposed an opposite strategy seeking low lateral (transverse) stiffness by connecting the structural elements flexibly (hinging and sliding). Under severe seismic inputs, these structures would accommodate racking without significant damage; this behaviour is highly resilient. The seismic resilience of this solution was numerically demonstrated in the well-known Daikai station (Kobe, Japan) and a station located in Chengdu (China). This paper is a continuation of these studies; it aims to extend, deepen, and ground this conclusion by performing a numerical parametric study on these two stations in a wide and representative set of situations characterised by the soil type, overburden depth, engineering bedrock position, and high- and lowlateral-stiffness of the stations. The performance indices are the racking displacement and the structural damage (quantified through concrete damage variables). The findings of this study validate the previous remarks and provide new insights.