We present experimental evidence of multiple blood flow configurations in a relatively simple microfluidic network under constant inlet conditions. We provide evidence of multistability and unsteady dynamics and find good agreement with a theoretical one- dimensional advection model for blood flow in microvascular networks that relies on the widely used laws for rheology and phase separation. We discuss the ramifications for microfluidic experiments and measurements using blood and implications for in vivo microcirculation. Our findings suggest that further modeling in microvascular networks should discard the usual assumption of unique, steady-state flow solutions, with crucial consequences regarding gas, nutrient, and waste transport.