With one GPU, if your script uses <50% of GPU memory, your best bet to increase GPU utilization is launching multiple scripts (processes).
In-process parallelization, using multiple cuda streams with replicated model modules may work but it is hard to write this correctly (in a nutshell, you must avoid blocking cuda operations [like copy() and item()], or use python threads)
And there is no way to do a tensor level parallelization on multiple input+parameter sets.