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We propose a filter bank multi-carriers (FBMC) passive optical network (PON) system based on 2-D multiple probabilistic shaping (MPS) distribution to achieve flexible and adjustable access bit-rates. The proposed PON can assign different probabilistic shaping schemes to different time-slots and subcarriers, thus improving the system flexibility and adjustability in both the time and frequency domains. Carrier-less amplitude and phase modulation are adopted to achieve the implementation of the intensity-modulation and direct-modulation applied in our proposed PON system. Moreover, for the first time, an experiment demonstrating MPS FBMC signal transmission over a 25-km standard single mode fiber in PON system is successfully carried out to verify the favorable performance. The bit error rate performance of different MPS time-slots at bit-rates of 23.665, 20.663, 17.666, and 15.481 Gbit/s are investigated. The received optical powers at the threshold for hard-decision forward error correction are −16.13, −16.94, −17.85, and −18.81 dBm, respectively. These experiment results indicate that our proposed MPS FBMC PON system can be flexible and adjustable in acquiring different and dynamic access bit-rates, which suggests a prospective solution for the next generation passive optical network.