How to increase the number of PCIe slots available?

Thank you all for your recommendations. Indeed, simply replacing the motherboard would be the cheapest solution for this use case. However:

• My motherboard ain't broke so I won't fix it. There is a certain risk associated with disassembling and reassembling the system, including moving over the CPU, and the memory sticks to the other motherboard.

• Replacing the motherboard also creates problems associated with software licenses that bind the software to the motherboard.

The number of PCIe slots can be increased by using PCIe splitters readily available from multiple manufacturers. Some PCIex16 splitters with GPU support:

GPU-Oriented x4 PCIe 4-Way Splitter

PCIe x16 Gen 3 Host Target Kit (3811)

Because the PCI slots have to correspond to cut-outs in the case, it is difficult-to-impossible to find a solution that will split your PCI lanes.

Even though you're still only looking for a single external PCI device, and the other lanes will be used got a storage device, if you look at the main board and the case, you'll notice there are only limited ways that an add-on decide could offer the functions you're imagining.

It is also likely to be cheaper to buy an entirely new main board with the features you want.

While you may not WANT to buy a new main board, what you want doesn't win against what's possible in this specific situation.