The realization of large-scale photonic circuits for quantum optics experiments at telecom wavelengths requires an increasing number of integrated detectors. Superconducting nanowire single photon detectors (SNSPDs) can be easily integrated onchip, and they can efficiently detect the light propagating inside waveguides. The thermal budget of cryostats poses a limit on the maximum number of elements that can be integrated on the same chip due to the thermal impact of the readout electronics. In this paper, we propose and implement a novel amplitude-multiplexing scheme allowing the efficient reading of several SNSPDs with only one readout port, thus enabling the realization of photonic circuits with a large number of modes.