Abstract This paper considers the Finch-Skea isotropic solution and extends
its domain to three different anisotropic interiors by using the
gravitational decoupling strategy in the context of
$f(\mathbb{R},\mathbb{T})$ gravitational theory. For this, we
consider that a static spherical spacetime is initially coupled with
the perfect matter distribution. We then introduce a Lagrangian
corresponding to a new gravitating source by keeping in mind that
this new source produces the effect of pressure anisotropy in the
parent fluid source. After calculating the field equations for the
total matter setup, we apply a transformation on the radial
component, ultimately providing two different systems of equations.
These two sets are solved independently through different
constraints that lead to some new solutions. Further, we consider an
exterior spacetime to calculate three constants engaged in the seed
Finch-Skea solution at the spherical interface. The estimated radius
and mass of a star candidate LMC X-4 are utilized to perform the
graphical analysis of the developed models. It is concluded that
only the first two resulting models are physically relevant in this
modified theory for all the considered parametric choices.