[riskable]

It's not so simple... The way GPU architecture works is that it needs as-fast-as-possible access to its VRAM. The concept of "overflow memory" for a GPU is your PC's RAM. Adding a secondary memory controller and equivalent DRAM to the card itself would only provide a trivial improvement over, "just using the PC RAM".

Point of fact: GPUs don't even use all the PCI Express lanes they have available to them! Most GPUs (even top of the line ones like Nvidia's 4090) only use about 8 lanes of bandwidth. This is why some newer GPUs are being offered with M.2 slots so you can add an SSD (https://press.asus.com/news/asus-dual-geforce-rtx-4060-ti-ss... ).