Recently, the Gravitational Decoupling through the Minimal Geometric Deformation was applied to study a mixture of a spherically symmetric internal solution of the Einstein gravitational equations with a polytropic fluid, giving interesting results of the energetic interchanges in the special case of the Tolman IV solution. In this work, we extend these newly introduced methods to the case of Tolman VII space-times that are currently considered as a convenient exact solution of Einstein equations representing relatively precisely realistic neutron stars.