This paper describes the winning system for SemEval-2020 task 7: Assessing Humor in Edited News Headlines. Our strategy is Stacking at Scale (SaS) with heterogeneous pre-trained language models (PLMs) such as BERT and GPT-2. SaS first performs fine-tuning on numbers of PLMs with various hyperparameters and then applies a powerful stacking ensemble on top of the fine-tuned PLMs. Our experimental results show that SaS outperforms a naive average ensemble, leveraging weaker PLMs as well as high-performing PLMs. Interestingly, the results show that SaS captured non-funny semantics. Consequently, the system was ranked 1st in all subtasks by significant margins compared with other systems.