Motivated by the rapid growth of modern signal processing applications and efficient mathematical tools that can handle multidimensional, nonstationary and shifted signals in a unified manner, this paper introduces a new transform, called the biquaternion offset linear canonical Stockwell transform (BiQOLCST). The proposed framework extends existing transform techniques and provides a flexible approach for analyzing complex signal structures. Several important properties of the transform are established, including linearity, anti-linearity, boundedness, shift and modulation properties, orthogonality relations and the reconstruction formula. In addition, Heisenberg, logarithmic and Donoho-Stark uncertainty principles are derived for the proposed transform, highlighting its inherent limits of simultaneous localization in different domains. These results also demonstrate the usefulness of the BiQOLCST in signal representation, analysis and recovery. Furthermore, signal reconstruction is investigated using the Donoho-Stark uncertainty principle, which provides theoretical conditions for the reliable recovery of signals from incomplete information. The potential applications in color image processing and in the analysis of non-stationary signals are explored.