The widespread adoption of large language models such as ChatGPT and Bard has led to unprecedented demand for these technologies.The burgeoning cost of inference for ever-increasing model sizes coupled with hardware shortages has limited affordable access and poses a pressing need for efficiency approaches geared towards high throughput and performance.Multi-input multi-output (MIMO) algorithms such as data multiplexing, offer a promising solution with a many-fold increase in throughput by performing inference for multiple inputs at the cost of a single input.Yet these approaches are not currently performant enough to be deployed in modern systems. We change that by developing MUX-PLMs, a class of deployable high throughput pre-trained language models (PLMs) trained with data multiplexing, that can be fine-tuned on any downstream task. Our novel multiplexing and demultiplexing modules proficiently entangle and disentangle inputs, and enable high-performance high throughput MUX-PLMs that are competitive with vanilla PLMs while achieving 2x/5x inference speedup with only a 1-4 % performance drop on a broad suite of tasks.