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Recent multimodal large language models (MLLMs) marry modality-specific vision or audio encoders with a shared text decoder. While the encoder is compute- intensive but memory-light, the decoder is the opposite, yet state-of-the-art serving stacks still time-multiplex these complementary kernels, idling SMs or HBM in turn. We introduce SpaceServe, a serving system that space-multiplexes MLLMs: it decouples all modality encoders from the decoder, and co-locates them on the same GPU using fine-grained SM partitioning available in modern runtimes. A cost-model-guided Space-Inference Scheduler (SIS) dynamically assigns SM slices, while a Time-Windowed Shortest-Remaining-First (TWSRFT) policy batches en- coder requests to minimise completion latency and smooth decoder arrivals. Evaluation shows that SpaceServe reduces time-per-output-token by 4.81× on average and up to 28.9× on Nvidia A100 GPUs. SpaceServe is available at https://github.com/gofreelee/SpaceServe