Event co-occurrences have been proved effective for event extraction (EE) in previous studies, but have not been considered for event argument extraction (EAE) recently. In this paper, we try to fill this gap between EE research and EAE research, by highlighting the question that “Can EAE models learn better when being aware of event co-occurrences?”. To answer this question, we reformulate EAE as a problem of table generation and extend a SOTA prompt-based EAE model into a non-autoregressive generation framework, called TabEAE, which is able to extract the arguments of multiple events in parallel. Under this framework, we experiment with 3 different training-inference schemes on 4 datasets (ACE05, RAMS, WikiEvents and MLEE) and discover that via training the model to extract all events in parallel, it can better distinguish the semantic boundary of each event and its ability to extract single event gets substantially improved. Experimental results show that our method achieves new state-of-the-art performance on the 4 datasets. Our code is avilable at https://github.com/Stardust-hyx/TabEAE.