This study delves into the repercussions of multiple slips within the Jeffrey fluid model, examining its impact on an unsteady magnetohydrodynamic viscoelastic buoyant nanofluid. This investigation is conducted in the context of Soret and radiation effects, encompassing a permeable stretching sheet. By employing suitable transformations, pertinent nonlinear differential equations are derived and subsequently addressed numerically using the finite element method. The analysis encompasses a thorough exploration of the influence of various controlling parameters on dimensionless quantities, including velocity, temperature, concentration, and nanofluid volume fraction profiles. Furthermore, it scrutinizes the effects of these parameters on dimensionless numbers such as local Nusselt, Sherwood, nano-particle Sherwood, and the local friction coefficient. An essential finding of this research is the examination of the impact of multiple slips, revealing that their presence amplifies the boundary layer flow.