In this study, we consider simultaneous connection routing in the three-stage switching fabric of the wavelength-spacewavelength architecture for elastic optical switches, which serve connections that can occupy different spectrum widths. Recently, the upper bound of the rearrangeability conditions was derived and proved for a switching fabric serving a limited number of connection rates. A control algorithm based on matrix decomposition was also proposed. In addition, the necessary and sufficient conditions were derived and proved for a switching fabric with a size of 2 × 2 serving only two connection rates, but only when the ratios between the connection rates and link capacity are integers. In this study, we extend these results to an arbitrary ratio between the connection rates and link capacity. The number of frequency slot units required in the interstage links is much lower than that in the strict-sense nonblocking switching fabrics. We also propose modifications to the control algorithm, which further reduces the number of frequency slot units required in many cases. Finally, we extend the results for 2 × 2 switching fabrics to those with a size of r × r.