accurately detect single photons, but saturate as soon as two photons arrive simultaneously. On the other hand, more linear watt meters, such as bolometers, are too noisy to accurately detect single microwave photons. Linear amplifiers probe non-commuting observables of a signal so that they must add noise and cannot be used to detect single photons, either. Here we experimentally demonstrate a microwave photon-multiplication scheme which combines the advantages of a single photon detector and a power meter by multiplying the incoming photon number by an integer factor. Our first experimental implementation achieves a n = 3-fold multiplication with 0.69 efficiency in a 116 MHz bandwidth up to a input photon rate of 400 MHz. It loses phase information but does not require any dead time or time binning. We expect an optimised device cascading such multipliers to achieve number-resolving measurement of itinerant photons with low dark count, which would offer new possibilities in a wide range of quantum sensing and quantum computing applications.