  This paper develops some new analytical solutions to the
$f(\mathbb{R},\mathbb{T})$ field equations through extended gravitational
decoupling. For this purpose, we take spherical anisotropic configuration as a
seed source and extend it to an additional source. The modified field equations
comprise the impact of both sources which are then decoupled into two distinct
sets by applying the transformations on $g_{tt}$ and $g_{rr}$ metric
potentials. The original anisotropic source is adorned by the first sector, and
we make it solvable by considering two different well-behaved solutions. The
second sector is in terms of an additional source and we adopt some constraints
to find deformation functions. The first constraint is the isotropization
condition which transforms the total fluid distribution into an isotropic
system only for a specific value of the decoupling parameter. The other
constraint is taken as the complexity-free fluid distribution. The unknown
constants are calculated at the hypersurface through matching conditions. The
preliminary information (mass and radius) of a compact star $4U 1820-30$ is
employed to analyze physical attributes of the resulting models. We conclude
that certain values of both the coupling as well as decoupling parameter yield
viable and stable solutions in this theory.
