This paper constructs three different anisotropic extensions of an existing isotropic solution to the modified field equations in the $f(\mathbb{R}, \mathbb{T})$ theory through gravitational decoupling. The authors start with a static sphere initially filled with an isotropic fluid and introduce a new gravitational source to produce anisotropy. The field equations are transformed to split them into two sets, one corresponding to the isotropic source and the other to the additional source. The isotropic solution is determined using Buchdahl's solution, while constraints on the additional source are applied to make the second system solvable. The constant triplet in Buchdahl's solution is calculated using matching criteria between the interior and exterior geometries. The mass and radius of the compact star LMC X-4 are used to analyze the physical relevance of the developed models. The resulting models II and III are found to be in good agreement with the acceptable conditions for the considered values of the parameters, showing stable behavior. The paper also discusses the formation of different anisotropic models and their physical acceptability conditions, including the existence of geometric singularities, finite and positive matter determinants, mass-radius ratio, surface redshift, energy conditions, and stability criteria.This paper constructs three different anisotropic extensions of an existing isotropic solution to the modified field equations in the $f(\mathbb{R}, \mathbb{T})$ theory through gravitational decoupling. The authors start with a static sphere initially filled with an isotropic fluid and introduce a new gravitational source to produce anisotropy. The field equations are transformed to split them into two sets, one corresponding to the isotropic source and the other to the additional source. The isotropic solution is determined using Buchdahl's solution, while constraints on the additional source are applied to make the second system solvable. The constant triplet in Buchdahl's solution is calculated using matching criteria between the interior and exterior geometries. The mass and radius of the compact star LMC X-4 are used to analyze the physical relevance of the developed models. The resulting models II and III are found to be in good agreement with the acceptable conditions for the considered values of the parameters, showing stable behavior. The paper also discusses the formation of different anisotropic models and their physical acceptability conditions, including the existence of geometric singularities, finite and positive matter determinants, mass-radius ratio, surface redshift, energy conditions, and stability criteria.