Yes and no.
PCIe has a concept of both lanes and ports. So the Southbridge has those 16 PCIe lanes configured to a single port. When you see a board that has 2 slots and it can be 1x PCIe16x or 2 PCIe8x it means the PCIe switch inside the southbridge is capable of dynamically configuring the port to lane assignments.
Just splitting the lanes physically will do no good. The PCIe switch inside the southbridge won't "know" there should be 3 or 7 more logical ports.
So what you need is a PCIE switch (a chip which can route PCIe lanes to ports) and that would require a custom PCB.
There are existing solutions which provide PCIe expansion but they are way to expensive. Here is one example:http://www.magma.com/expressbox16basic.asp
It adds 16 PCIe slots in an external chasis from a single 16x port. So hypothetically take a MB w/ 4 PCIe 16x slots connect each one to a 16 bay expansion chasis and gain 64 slots for GPUs.
Two problems. One the chassis and expander is an insane $4500. Two AMD stupidly limits you to 8 GPU.
Given the 8 GPU limit I have found the easiest, fastest, and most efficient setup is a motherboard with 3x 16x slots spaced two spaces apart and use 3x 5970s for 6 total GPU. No other method seems to come close to that in terms of cost.
OK so it's possible, just expensive.
The trouble with *your* solution DAT is that finding 5970 cards has become rather difficult, not to mention rather expensive in hash per £.
The video card vendors, certainly here in the UK, seem to know damn well that bitcoin miners want the 58xx/5970 cards at any cost and are pumping up the prices. The cheapest I've seen for a usable card (over 200 MH/s for me) is £80 for the 5770. At those prices, when the dual-GPU single cards are costing £600 or more, it's almost worth buying two of my favourite Gigabyte 4-slot boards and running 8 of the 5770s (which all reliably clock up to 220 MH/s each - the disadvantage being space, and potentially efficiency.
I must say that I'm surprised at the cost of the 'lane splitter' solutions. Entire logic boards (like my beloved Gigabyte H61M-D2-B3) cost around £55 inc VAT these days. There's a southbridge on there which splits the PCIe bandwidth into one x16 slot and three x1 slots. Hence the chip logic to split PCIe lanes into different configurations can't be *that* expensive, can it?
I've got an Asus logic board which I've given up on - I bought it for its 5 PCIe slots - and three well-spaced x16 slots (it'd be a candidate for your preferred format, since you'd get your three 5970s onto the board with no extender cables required). A feature in its BIOS allows you to split the bandwidth across the physical PCIe slots - you can disable the two x1 slots and give maximum bandwidth (x16, x8, x8) for three GPUs, or you can have two full-fat x16s with the rest disabled, or the 'x1' config I was trying to get to work, where all slots are available at x1 bandwidth.
This board caused me so many problems (trying to get all 5 slots working with GPUs) that I've taken the CPU out and put it in another Gigabyte board - that's four Gigabyte boards I've got now in my farm
They just work.
However, this Asus board suggests that the BIOS can configure which slots get however many PCIe lanes... so if the software and hardware can already split PCIe bandwidth across the available slots, why are these extension systems so damned expensive?
After all, if the solution I want costs thousands, then I can just bite my tongue and order a few of those damn 'extreme gamer' Big Bong boards which already have 7 PCIe slots on the board (and probably waste 50W or so just running the logic board, requiring more powerful PSUs as well, adding to the cost)