This paper introduces a modification of phase transform on singular value decomposition (SVD-PHAT) to localize multiple sound sources. This work aims to improve localization accuracy and keeps the algorithm complexity low for real-time applications. This method relies on multiple scans of the search space, with projection of each low-dimensional observation onto orthogonal subspaces. We show that this method localizes multiple sound sources more accurately than discrete SRP-PHAT, with a reduction in the Root Mean Square Error up to 0.0395 radians.