This paper is devoted to the computation of anisotropic extensions of the Tolman IV solution through the extended gravitational decoupling scheme in the background of \(f({\mathbb {R}},T)\) gravity where \({\mathbb {R}}\) represents the Ricci scalar and T is the trace of the energy–momentum tensor. In this regard, we have picked a linear model of the form \(f({\mathbb {R}},T)={\mathbb {R}}+2\chi T\) where \(\chi\) connects geometry to the matter sector. The extended gravitational decoupling method involves a decoupling parameter that controls the magnitude of the induced anisotropy. Deformations in radial and temporal metric components decompose the field equations into two subsystems. One of these sets corresponds to the isotropic solution, whereas the other is solved using additional constraints. We analyze the results graphically and explore the compactness, redshift, equilibrium and stability of the acquired anisotropic solutions for the star candidate Her X-1. It is found that the decoupling technique in the context of \(f({\mathbb {R}},T)\) gravity delivers physically acceptable solutions portraying realistic spherical configurations.
