Suppose, not hypothetically, that you're switching from one mirrored set of M.2 NVMe drives to another mirrored set of M.2 NVMe drives, and so would like to have three or four NVMe drives in your desktop at the same time. Sadly, you already have one of your two NVMe drives on a PCIe card, so you'd like to get a single PCIe card that handles two or more NVMe drives. If you look around today, you'll find two sorts of cards for this; ones that are very expensive, and ones that are relatively inexpensive but require that your system supports a feature that is generally called PCIe bifurcation.

NVMe drives are PCIe devices, so a PCIe card that supports a single NVMe drive is a simple, more or less passive thing that wires four PCIe lanes and some other stuff through to the M.2 slot. I believe that in theory, a card could be built that only required x2 or even x1 PCIe lanes, but in practice I think all such single drive cards are physically PCIe x4 and so require a physical x4 or better PCIe slot, even if you'd be willing to (temporarily) run the drive much slower.

A PCIe card that supports more than one M.2 NVMe drive has two options. The expensive option is to put a PCIe bridge on the card, with the bridge (probably) providing a full set of PCIe lanes to the M.2 NVMe drives locally on one side and doing x4, x8, or x16 PCIe with the motherboard on the other. In theory, such a card will work even at x4 or x2 PCIe lanes, because PCIe cards are supposed to do that if the system says 'actually you only get this many lanes' (although obviously you can't drive four x4 NVMe drives at full speed through a single x4 or x2 PCIe connection).

The cheap option is to require that the system be able to split a single PCIe slot into multiple independent groups of PCIe lanes (I believe these are usually called links); this is PCIe bifurcation. In PCIe bifurcation, the system takes what is physically and PCIe-wise an x16 slot (for example) and splits it into four separate x4 links (I've seen this sometimes labeled as 'x4/x4/x4/x4'). This is cheap for the card because it can basically be four single M.2 NVMe PCIe cards jammed together, with each set of x4 lanes wired through to a single M.2 NVMe slot. A PCIe card for two M.2 NVMe drives will require an x8 PCIe slot bifurcated to two x4 links; if you stick this card in an x16 slot, the upper 8 PCIe lanes just get ignored (which means that you can still set your BIOS to x4/x4/x4/x4).

As covered in, for example, this Synopsys page, PCIe bifurcation isn't something that's negotiated as part of bringing up PCIe connections; a PCIe device can't ask for bifurcation and can't be asked whether or not it supports it. Instead, the decision is made as part of configuring the PCIe root device or bridge, which in practice means it's a firmware ('BIOS') decision. However, I believe that bifurcation may also requires hardware support in the 'chipset' and perhaps the physical motherboard.

I put chipset into quotes because for quite some time, some PCIe lanes come directly from the CPU and only some others come through the chipset as such. For example, in desktop motherboards, the x16 GPU slot is almost always driven directly by CPU PCIe lanes, so it's up to the CPU to have support (or not have support) for PCIe bifurcation of that slot. I don't know if common desktop chipsets support bifurcation on the chipset PCIe slots and PCIe lanes, and of course you need chipset-driven PCIe slots that have enough lanes to be bifurcated in the first place. If the PCIe slots driven by the chipset are a mix of x4 and x1 slots, there's no really useful bifurcation that can be done (at least for NVMe drives).

If you have a limited number of PCIe slots that can actually support x16 or x8 and you need a GPU card, you may not be able to use PCIe bifurcation in practice even if it's available for your system. If you have only one PCIe slot your GPU card can go in and it's the only slot that supports bifurcation, you're stuck; you can't have both a bifurcated set of NVMe drives and a GPU (at least not without a bifurcated PCIe riser card that you can use).

(This is where I would start exploring USB NVMe drive enclosures, although on old desktops you'll probably need one that doesn't require USB-C, and I don't know if a NVMe drive set up in a USB enclosure can later be smoothly moved to a direct M.2 connection without partitioning-related problems or other issues.)

(This is one of the entries I write to get this straight in my head.)

Sidebar: Generic PCIe riser cards and other weird things

The traditional 'riser card' I'm used to is a special proprietary server 'card' (ie, a chunk of PCB with connectors and other bits) that plugs into a likely custom server motherboard connector and makes a right angle turn that lets it provide one or two horizontal PCIe slots (often half-height ones) in a 1U or 2U server case, which aren't tall enough to handle PCIe cards vertically. However, the existence of PCIe bifurcation opens up an exciting world of general, generic PCIe riser cards that bifurcate a single x16 GPU slot to, say, two x8 PCIe slots. These will work (in some sense) in any x16 PCIe slot that supports bifurcation, and of course you don't have to restrict yourself to x16 slots. I believe there are also PCIe riser cards that bifurcate an x8 slot into two x4 slots.

Now, you are perhaps thinking that such a riser card puts those bifurcated PCIe slots at right angles to the slots in your case, and probably leaves any cards inserted into them with at least their tops unsupported. If you have light PCIe cards, maybe this works out. If you don't have light PCIe cards, one option is another terrifying thing, a PCIe ribbon cable with a little PCB that is just a PCIe slot on one end (the other end plugs into your real PCIe slot, such as one of the slots on the riser card). Sometimes these are even called 'riser card extenders' (or perhaps those are a sub-type of the general PCIe extender ribbon cables).

Another PCIe adapter device you can get is an x1 to x16 slot extension adapter, which plugs into an x1 slot on your motherboard and has an x16 slot (with only one PCIe lane wired through, of course). This is less crazy than it sounds; you might only have an x1 slot available, want to plug in a x4, x8, or x16 card that's short enough, and be willing to settle for x1 speeds. In theory PCIe cards are supposed to still work when their lanes are choked down this way.