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Large-scale simulations of plasmas are essential for advancing our understanding of fusion devices, space, and astrophysical systems. Particle-in-Cell (PIC) codes have demonstrated their success in simulating numerous plasma phenomena on HPC systems. Today, flagship supercomputers feature multiple GPUs per compute node to achieve unprecedented computing power at high power efficiency. PIC codes require new algorithm design and implementation for exploiting such accelerated platforms. In this work, we design and optimize a three-dimensional implicit PIC code, called sputniPIC, to run on a general multi-GPU compute node. We introduce a particle decomposition data layout, in contrast to domain decomposition on CPU-based implementations, to use particle batches for overlapping communication and computation on GPUs. sputniPIC also natively supports different precision representations to achieve speed up on hardware that supports reduced precision. We validate sputniPIC through the well-known GEM challenge and provide performance analysis. We test sputniPIC on three multi-GPU platforms and report a 200-800x performance improvement with respect to the sputniPIC CPU OpenMP version performance. We show that reduced precision could further improve performance by 45% to 80% on the three platforms. Because of these performance improvements, on a single node with multiple GPUs, sputniPIC enables large-scale three-dimensional PIC simulations that were only possible using clusters.