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Multiple blind sound source localization is the key technology for a myriad of applications such as robotic navigation and indoor localization. However, existing solutions can only locate a few sound sources simultaneously due to the limitation imposed by the number of microphones in an array. To this end, this paper proposes a novel multiple blind sound source localization algorithms using Source seParation and BeamForming (SPBF). Our algorithm overcomes the limitations of existing solutions and can locate more blind sources than the number of microphones in an array. Specifically, we propose a novel microphone layout, enabling salient multiple source separation while still preserving their arrival time information. After then, we perform source localization via beamforming using each demixed source. Such a design allows minimizing mutual interference from different sound sources, thereby enabling finer AoA estimation. To further enhance localization performance, we design a new spectral weighting function that can enhance the signal-to-noise-ratio, allowing a relatively narrow beam and thus finer angle of arrival estimation. Simulation experiments under typical indoor situations demonstrate a maximum of only <inline-formula><math display="inline"><semantics><msup><mn>4</mn><mo>∘</mo></msup></semantics></math></inline-formula> even under up to 14 sources.