We investigate the viscous finger instabilities that arise at two interfaces formed by the sequential injection of three Newtonian fluids into a rectangular Hele-Shaw cell. For this purpose, we use linear stability analysis and develop a set of first-order ordinary differential equations, formulated to describe the evolution of the perturbations at the interfaces. Based on this approach, we evaluate the problem in a perturbative manner, with emphasis on the analysis of the coupling effect between the two interfaces, quantified by the thickness of the intermediate fluid, in the linear flow regime. In parallel to the theoretical study, we performed a series of experimental tests to investigate the growth of Saffman-Taylor instabilities in the three-fluid, two-interface system. The construction of the experimental device is described in detail, including all the adaptations made to the apparatus throughout this study. The results indicate that the interaction between the interfaces is governed by the coupling level between them, influencing both the time required for instability development and the morphology of the viscous fingers. This effect was initially identified through linear stability analisys. Then, we experimentally verified that manipulating the intermediate fluid thickness allows for the delay of instabilities development, and that these effects persist in the nonlinear regime. Such findings indicate that the volume of the intermediate phase can be controlled to minimize the deformations of the interfaces and, consequently, increase the efficiency of the displacement process. This phenomenon may be relevant to the industrial sector, serving as a strategy for enhanced oil recovery (EOR) processes. We highlight, in particular, the applicability of these methods in alternating injection processes and in chemical methods, in which fluids are pumped sequentially into porous media to optimize the extraction process.