Storing and delaying optical signals plays a crucial role in data centers, phased array antennas, communication, and future computing architectures. Here, we show a delay scheme based on cascaded Brillouin light storage that achieves multi-stage delay at arbitrary positions within a photonic integrated circuit. Importantly these multiple resonant transfers between the optical and acoustic domain are controlled solely via external optical control pulses, allowing cascading of the delay without the need of aligning multiple structural resonances along the optical circuit.