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In this paper, we introduce MINTIME, a video deepfake detection approach that captures spatial and temporal anomalies and handles instances of multiple people in the same video and variations in face sizes. Previous approaches disregard such information either by using simple a-posteriori aggregation schemes, i.e., average or max operation, or using only one identity for the inference, i.e., the largest one. On the contrary, the proposed approach builds on a Spatio-Temporal TimeSformer combined with a Convolutional Neural Network backbone to capture spatio-temporal anomalies from the face sequences of multiple identities depicted in a video. This is achieved through an Identity-aware Attention mechanism that attends to each face sequence independently based on a masking operation and facilitates video-level aggregation. In addition, two novel embeddings are employed: (i) the Temporal Coherent Positional Embedding that encodes each face sequence's temporal information and (ii) the Size Embedding that encodes the size of the faces as a ratio to the video frame size. These extensions allow our system to adapt particularly well in the wild by learning how to aggregate information of multiple identities, which is usually disregarded by other methods in the literature. It achieves state-of-the-art results on the ForgeryNet dataset with an improvement of up to 14% AUC in videos containing multiple people and demonstrates ample generalization capabilities in cross-forgery and cross-dataset settings. The code is publicly available at https://github.com/davide-coccomini/MINTIME-Multi-Identity-size-iNvariant-TIMEsformer-for-Video-Deepfake-Detection.