In this paper, we describe our submission for the OCAST4 2020 shared tasks on offensive language and hate speech detection in the Arabic language. Our solution builds upon combining a number of deep learning models using pre-trained word vectors. To improve the word representation and increase word coverage, we compare a number of existing pre-trained word embeddings and finally concatenate the two empirically best among them. To avoid under- as well as over-fitting, we train each deep model multiple times, and we include the optimization of the decision threshold into the training process. The predictions of the resulting models are then combined into a tuned ensemble by stacking a classifier on top of the predictions by these base models. We name our approach “ESOTP” (Ensembled Stacking classifier over Optimized Thresholded Predictions of multiple deep models). The resulting ESOTP-based system ranked 6th out of 35 on the shared task of Offensive Language detection (sub-task A) and 5th out of 30 on Hate Speech Detection (sub-task B).