Due to data privacy constraints, data sharing among multiple centers is restricted. Continual learning, as one approach to peer-to-peer federated learning, can promote multicenter collaboration on deep learning algorithm development by sharing intermediate models instead of training data. This work aims to investigate the feasibility of continual learning for multicenter collaboration on an exemplary application of brain metastasis identification using DeepMedic. 920 T1 MRI contrast enhanced volumes are split to simulate multicenter collaboration scenarios. A continual learning algorithm, synaptic intelligence (SI), is applied to preserve important model weights for training one center after another. In a bilateral collaboration scenario, continual learning with SI achieves a sensitivity of 0.917, and naive continual learning without SI achieves a sensitivity of 0.906, while two models trained on internal data solely without continual learning achieve sensitivity of 0.853 and 0.831 only. In a seven-center multilateral collaboration scenario, the models trained on internal datasets (100 volumes each center) without continual learning obtain a mean sensitivity value of 0.699. With single-visit continual learning (i.e., the shared model visits each center only once during training), the sensitivity is improved to 0.788 and 0.849 without SI and with SI, respectively. With iterative continual learning (i.e., the shared model revisits each center multiple times during training), the sensitivity is further improved to 0.914, which is identical to the sensitivity using mixed data for training. Our experiments demonstrate that continual learning can improve brain metastasis identification performance for centers with limited data. This study demonstrates the feasibility of applying continual learning for peer-to-peer federated learning in multicenter collaboration.