Accurate decoding of perceptual information from brain signals is crucial in real-world BCI applications. While existing decoding methods work well in static, single-subject cases, more versatile, multi-subject decoding methods should be developed for achieving scalable and transferable BCI systems. In practice, it is not straightforward to record brain signals using the same recording equipment from a large number of subjects. If a pretrained decoder is not robust to subject or channel shifts, it cannot be applied to data from novel subjects and even from trained subjects when the recording equipment changes. In this work, we study brain decoding across multiple subjects with a different number of recording channels and channel location shifts. We consider channel-agnostic brain decoding as a multi-instance learning problem, where each input is seen as a set of instances. We propose a novel decoder architecture based on three building blocks: A channel-wise transform, an across-channel transform, and multi-channel pooling. We conduct a thorough experiment on our multi-subject electrocorticography (ECoG) classification dataset to verify the effectiveness of our proposed methods against other baseline architectures. Our results show that, even without any explicit spatial information about channels, our proposed architecture with channel permutation invariance and channel interactions work well in channel-agnostic multi-subject brain decoding.