Superposition approaches have generally been proposed to create a dynamic rheological map to access colloidal glassy dynamics beyond experimental time windows. However, the validity of the superposition approaches in colloids near the glass transition is questionable owing to the well-known emergence of a β-relaxation process there. Here, we employ a time-concentration superposition (TCS) approach, analogous to time-temperature superposition and TCS approaches in molecular systems, utilizing a combination of macroscopic rheological experiments and microscopic Brownian dynamics simulations, where concentration jumps are performed by a sudden growth of particle size [soft polystyrene-poly (N-isopropylacrylamide) particles in experiment and nearly hard spheres in simulation] at a fixed number of particles. We have examined whether a characteristic master curve can be obtained through horizontal and vertical shifting of the dynamic data, finding that TCS does not hold for either the experimental or simulation systems. We identify the origin of this breakdown as not only the emergence of a strong β-relaxation process but also its overlap with the α relaxation in both the experimental soft-sphere and the simulated nearly hard-sphere colloids near the glass transition concentration. Further understanding of the lack of validity of TCS results from analysis of both experimental and simulation data in the framework of the Baumgaertel-Schausberger-Winter (BSW) relaxation spectrum which provide a means to determine the concentration dependences of both the α and the β relaxations, which seem to follow TCS themselves.