Background: Teachers' team innovativeness--the collective capacity of teaching teams to generate, adopt, and implement new ideas and practices--is increasingly recognized for its role in enhancing instructional methods and fostering school innovation. However, empirical research identifying its predictors remains limited, particularly within large-scale educational contexts. Prior studies often analyzed a restricted set of variables using traditional multilevel models, which may not fully capture the complexity inherent in such data structures. Methods: This study utilized data from the Teaching and Learning International Survey (TALIS) 2018, encompassing responses from 2895 Korean middle school teachers and 163 principals. To address the multilevel structure of the data and perform comprehensive variable selection, we employed glmmLasso--a penalized regression technique that integrates generalized linear mixed models with LASSO penalties. This approach allowed for the identification of important predictors of teachers' team innovativeness across 571 explanatory variables. Additionally, a simulation study was conducted to evaluate the performance of glmmLasso in comparison to traditional LASSO and elastic net (Enet) methods regarding predictive accuracy and variable selection. Results: The application of glmmLasso resulted in a more parsimonious model, selecting considerably fewer variables while maintaining predictive performance comparable to that of LASSO and Enet. Fourteen key predictors of teachers' team innovativeness were identified, predominantly exhibiting positive associations and encompassing factors such as teacher collaboration, self-efficacy, and supportive school climate. Notably, the variable representing shared responsibility for school issues demonstrated a negative association with team innovativeness. The simulation study further supported glmmLasso's superior accuracy in identifying true predictors and reducing false positives, particularly at the school level. Conclusions: This study contributes both methodologically and substantively by demonstrating the efficacy of glmmLasso in analyzing large-scale, nested educational data to uncover important predictors of teachers' team innovativeness. The findings offer actionable insights for educational policymakers and school leaders aiming to cultivate innovative teaching teams through strategies that enhance teacher collaboration, bolster self-efficacy, and foster a supportive school climate. Future research should explore the applicability of glmmLasso across diverse educational contexts and consider the development of advanced penalized regression techniques to address challenges such as the optimal selection count thresholds and the appropriate size of ICC within multilevel data structures.