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We propose and demonstrate a design for a lossless rectangular-passband multiplexer with improved passband characteristics. It consists of a waveguide grating router (WGR) synchronized to a three-arm interferometer. It is similar to our previous design of synchronizing a WGR to a two-arm interferometer, except now the passband has even sharper corners. We also show that three is the maximum number of arms for the input interferometer if one wishes to have a compact layout.