<p>This study constructs a model of a compact, anisotropic star formed by two interacting fluids: the fluid of Einstein’s static universe and an additional source with a Tolman IV-type complexity. Using an extended gravitational decoupling method that allows energy exchange between fluids, the resulting stellar configuration is shown to be physically viable and stable. The model describes highly compact stars with masses between roughly two times the mass of the Sun. Energy transfer between the two fluids intensifies as the star becomes more compact, while its direction depends on the properties of the Einstein’s universe fluid. When the star is perturbed non-radially, internal fractures such as cracking and overturning may appear, except in less compact stars below a specific threshold. Under radial perturbations, the star oscillates with positive frequencies, confirming its dynamical stability. Overall, the coexistence of a cosmological fluid with a source of controlled complexity leads to a stable, highly compact anisotropic stellar model where internal complexity, energy exchange, and stability are closely linked.</p>