The transition-edge sensor (TES) is a mature, high-resolution x-ray spectrometer technology that provides a much higher efficiency than dispersive spectrometers such as gratings and crystal spectrometers. As larger arrays are developed, time-division multiplexing schemes operating at MHz frequencies are being replaced by microwave SQUID multiplexers using frequency-division multiplexing at GHz frequencies. However, the multiplexing factor achievable with microwave SQUIDs is limited by the high slew rate on the leading edge of x-ray pulses. In this paper, we propose a new multiplexing scheme for high-slew-rate TES x-ray calorimeters: the spread-spectrum SQUID multiplexer, which has the potential to enable higher multiplexing factors, especially in applications with lower photon-arrival rates.