We propose new techniques to enhance the stability properties of standard explicit numerical techniques for solving systems of stochastic differential equations (SDEs). The core idea is to modify the coefficients of conventional explicit methods, replacing them with matrices that depend on the Jacobian of the drift term of the SDE. These Jacobian-dependent schemes can also be applied to the numerical solution of stochastic partial differential equations (SPDEs) via the method of lines, where they address the spatially discretized problem [6]. The proposed nu- merical methods are developed by integrating existing explicit techniques [3, 4, 5] with TASE (Time-Accurate and Highly-Stable Explicit) operators [1, 2]. The primary objective of this in- tegration is to improve the stability properties of the selected methods while preserving their explicit nature. However, since these new schemes require inverting Jacobian-dependent ma- trices at each time step, they effectively function as linearly implicit methods. This research introduces TASE stochastic Runge-Kutta methods with a strong order of convergence p = 1 and p = 1.5. We conduct numerical experiments to validate the theoretical properties of the proposed methods. This Minisymposium falls within the activities of PRIN-MUR 2022 project 20229P2HEA ”Stochas- tic numerical modelling for sustainable innovation”, CUP: E53D23017940001, granted by the Italian Ministry of University and Research within the framework of the Call relating to the scrolling of the final rankings of the PRIN 2022 call and the PRIN PNRR 2022 project BAT- MEN (BATtery Modeling, Experiments & Numerics), CUP: F53D23010020001.