This paper studies the synthesis of between-leg coupling schemes for passively-adaptive non-redundant legged robots. Highly actuated legged robots can arbitrarily locate their feet relative to their bodies through active control, but often wind up kinematically over-constrained following ground contact, requiring complex redundant control for stable locomotion. The use of passive sprung joints can provide some minimal passive adaptability to terrain, but it is limited to relatively low terrain variability due to practical travel limits. In this paper, using a 4-RR platform as case study, we show that implementing parallel adaptive couplings between legs of a stance platform can yield substantial passive adaptability to rough terrain while still ensuring that the body is fully constrained in stance. This study uses screw theory-based mobility analysis methods to determine the number of constraints required to control the stance platform. Several coupling schemes are then considered and evaluated through a simulation of their stance capabilities over arbitrary terrain. An experimental validation of these simulation results is presented; it demonstrates the viability of the proposed scheme for passive adaptability.