Plasticity in crystalline materials is the result of the motion and interaction of dislocations. Continuum Dislocation Dynamics (CDD), which relies on conservation laws and balance equations for alignment tensors, offers a promising approach by providing an efficient continuum-level description of dislocation behavior, reducing the computational complexity compared to Discrete Dislocation Dynamics (DDD). This approach has been particularly successful in single-slip systems. However, CDD faces challenges in multi-slip systems, where dislocations interact across multiple systems. In these cases, the precise evolution of alignment tensors during complex interactions remains insufficiently understood, limiting the CDD model’s predictive capacity. To address these challenges and develop a more comprehensive description of plasticity, advanced data-driven methods based on DDD data are employed to estimate and incorporate multi-slip system interaction terms in the evolution equations of the alignment tensors. In the current work, a Koopman-based lifting technique for infinite-dimensional systems is applied to identify and model these interaction terms. This method uses a generalized extended dynamic mode decomposition for infinite-dimensional systems alongside the infinitesimal generator of the Koopman operator, which provides a promising tool for the extraction of missing source terms in the evolution equations directly from data. A reduced system is employed to gain insights into the possible slip system interaction terms that can occur in CDD. Building upon this, interaction terms can be estimated for the full model. By matching these identified terms to empirical data, the model ensures that all relevant interactions are accounted for within the CDD framework, allowing for a more accurate representation of multi-slip dynamics. Capturing these interaction terms is crucial, as it completes the evolution equations for alignment tensors and brings the CDD framework closer to a fully predictive model of plasticity.