Flexure-based linear stages have become prevalent in precision engineering; however, most designs suffer from parasitic shifts that degrade positioning accuracy. Conventional solutions to mitigate these parasitic motions often compromise support stiffness, reduce motion range, and increase structural complexity. This study presents a novel family of flexure-based rectilinear-motion stages using coupled n-RRR planar parallel mechanisms, achieving extremely low parasitic shifts while addressing the forementioned limitations. Four design variants are selected and analyzed via Finite Element Method (FEM) simulations, evaluating parasitic shifts, stroke, and support stiffness. The most precise configuration, a 4-RRR rectilinear stage having kinematic chains coupled via two Watt linkages, exhibits a lateral shift smaller than 0.258 µm and an in-plane parasitic rotation smaller than 12.6 µrad over a 12 mm stroke. Experimental validation using a POM prototype confirms the high positioning precision and support stiffness properties. In addition, a silicon prototype incorporating thermally preloaded buckling beams is investigated to reduce its translational stiffness. Experimental results show a translational stiffness reduction of 98% in the monostable configuration and 112% in the bistable configuration (i.e., negative stiffness), without support stiffness reduction. These results highlight the potential of the proposed mechanisms for a wide range of precision applications, offering a scalable and high-accuracy solution for micro-and nano-positioning systems.