We propose a parallel multi delay (PMD) carrier-assisted differential detection (CADD) receiver for the first time, including PMD asymmetric-CADD (PMD A-CADD) and PMD symmetric-CADD (PMD S-CADD). The transfer function of the PMD CADD receiver is optimized by expanding the number of optical delays to a general selection, thereby suppressing the signal-signal beat interference (SSBI). As a result, the required carrier-to-signal power ratio (CSPR) is reduced, and the optical signal-to-noise ratio (OSNR) sensitivity is drastically improved. Two schemes for further mitigation of residual SSBI are introduced, namely SSBI iterative cancellation algorithm and the increased guard band mitigation method. For SSBI iterative cancellation algorithm, by optimizing the number of optical delays, the optimal CSPR for the P6D A-CADD and the P5D S-CADD can be reduced to −1 dB, the required number of iterations is only 3, and compared with the parallel dual delay-based asymmetric-CADD (PDD A-CADD) receiver, the OSNR sensitivity is improved by about 4.5 dB. For the increased guard band mitigation method, 2.34 GHz and 3.16 GHz guard band are required for the P6D A-CADD and the P5D S-CADD to meet the 7% FEC threshold at 0 dB CSPR.