This paper presents the best-performing solution to the SemEval 2023 Task 3 on the subtask 3 dedicated to persuasion techniques detection. Due to a high multilingual character of the input data and a large number of 23 predicted labels (causing a lack of labelled data for some language-label combinations), we opted for fine-tuning pre-trained transformer-based language models. Conducting multiple experiments, we find the best configuration, which consists of large multilingual model (XLM-RoBERTa large) trained jointly on all input data, with carefully calibrated confidence thresholds for seen and surprise languages separately. Our final system performed the best on 6 out of 9 languages (including two surprise languages) and achieved highly competitive results on the remaining three languages.