Basement excavation inevitably causes stress changes in the ground, leading to soil movements that may affect the serviceability and safety of adjacent tunnels. Despite paying much attention to the basement–tunnel interaction, previous research has mainly focused on the influence of tunnel location in relation to the basement, tunnel stiffness, and excavation geometry. The effects of sand density and basement wall stiffness on nearby tunnels due to excavation, however, have so far been neglected. A series of three-dimensional centrifuge tests were thus carried out in this study to investigate these effects on the complex basement–tunnel interaction. Moreover, three-dimensional numerical analyses and a parametric study by adopting a hypoplastic sand model were conducted to improve the fundamental understanding of this complex problem, and calculation charts were developed as a design tool. When the basement was constructed directly above the existing tunnel, excavation-induced heave and strain were more sensitive to a change in soil density in the transverse direction than that in the longitudinal direction of the tunnel. Because a looser sand possesses smaller soil stiffness around the tunnel, the maximum tunnel elongation and transverse tensile strain increased by more than 20% as the relative sand density decreased by 25%. Moreover, the tensile strain induced along the longitudinal direction was insensitive to the stiffness of the retaining wall, but the tensile strain induced along the transverse direction was significantly reduced by a stiff wall. When the basement was constructed at the side of the existing tunnel, the use of a diaphragm wall reduced the maximum settlements and tensile strains induced in the tunnel by up to 22% and 58%, respectively, compared with the use of a sheet pile wall. Under the same soil density and wall stiffness, excavation-induced maximum movement and tensile strains in the tunnel located at a side of the basement were about 30% of the measured values in the tunnel located directly beneath the basement centre.