While large language models (LLMs) have enabled learning knowledge from the pre-training corpora, the acquired knowledge may be fundamentally incorrect or outdated over time, which necessitates rectifying the knowledge of the language model (LM) after the training. A promising approach involves employing a hyper-network to generate parameter shift, whereas existing hyper-networks suffer from inferior scalability in synchronous editing operation amount (Hase et al., 2023b; Huang et al., 2023). For instance, Mitchell et al. (2022) mimics gradient accumulation to sum the parameter shifts together, which lacks statistical significance and is prone to cancellation effect. To mitigate the problem, we propose the MAssive Language Model Editing Network (MALMEN), which formulates the parameter shift aggregation as the least square problem, subsequently updating the LM parameter using the normal equation. To accommodate editing multiple facts simultaneously with limited memory budgets, we separate the computation on the hyper-network and LM, enabling arbitrary batch size on both neural networks. Our method is evaluated by editing up to thousands of facts on LMs with different architectures, i.e., BERT-base, GPT-2, and GPT-J (6B), across various knowledge-intensive NLP tasks, i.e., closed book fact-checking and question answering. Remarkably, MALMEN is capable of editing hundreds of times more facts than MEND (Mitchell et al., 2022) with the identical hyper-network architecture and outperforms editor specifically designed for GPT, i.e., MEMIT (Meng et al., 2023).