  In the work, we present investigation on decoupling gravitational sources
under the framework of $f(R,T)$ gravity. Basically the complete geometric
deformation technique has been employed here which facilitates finding exact
solutions to the anisotropic astrophysical system smoothly without imposing any
particular ansatz for deformation function. Along with this we have also used
5-dimensional Euclidean spacetime in order to describe the embedding Class I
spacetime for getting a solvable spherical physical system. The solutions thus
obtained show physically interesting as well as viable with new possibilities
to sought for. Especially, from the present investigation it is worthy to note
that the mixture $f(R,T)$ + CGD translate the scenario beyond the pure GR realm
and hence clearly helps to enhance the features of the interior astrophysical
aspects of compact stellar objects. Therefore to check the physical
acceptability and stability of the stellar system based on the obtained
solutions, we have performed a few physical tests which satisfy all the
stability criteria, including nonsingular nature of the density as well as
pressure.
