Traditional sampling involves encoding a signal through (time, value)-pairs. In contrast, time encoding machines (TEMs) characterize a signal by recording time points which depend on the integral of the signal over time. We study multi-channel TEMs where channels have shifted values for their integrators. We show that M channels can enable recovery of bandlimited signals with M times the bandwidth of that allowed in the single channel case. Moreover, our recovery algorithm is linear, even when the shift between the integrators of the TEMs is unknown. This is in stark contrast to traditional multi-channel sampling, where complicated non-linear methods are required to recover the unknown time shift between channels.