Can't you offload KV to system RAM, or even storage? It would make it possible to run with longer contexts, even with some overhead. AIUI, local AI frameworks include support for caching some of the KV in VRAM, using a LRU policy, so the overhead would be tolerable.
With that said, people are trying to extend VRAM into system RAM or even NVMe storage, but as soon as you hit the PCI bus with the high bandwidth layers like KV cache, you eliminate a lot of the performance benefit that you get from having fast memory near the GPU die.
Only useful for prefill (given the usual discrete-GPU setup; iGPU/APU/unified memory is different and can basically be treated as VRAM-only, though a bit slower) since the PCIe bus becomes a severe bottleneck otherwise as soon as you offload more than a tiny fraction of the memory workload to system memory/NVMe. For decode, you're better off running entire layers (including expert layers) on the CPU, which local AI frameworks support out of the box. (CPU-run layers can in turn offload to storage for model parameters/KV cache as a last resort. But if you offload too much to storage (insufficient RAM cache) that then dominates the overhead and basically everything else becomes irrelevant.)"