I'm pretty sure there are add-in cards that can do bifurcation, meant for use with motherboards that don't support bifurcation normally (or have more limited bifurcation options).
Unfortunately PCIe lane bifurcation and PCIe lane switching often get mixed up, even if they are not the same.
It doesn't help, that they can in fact be combined...
Bifurcation is splitting the lanes of a slot into smaller pieces via a 'purely' mechanical or non-logical means (=cheap!). There might be some components, even re-timers, but logically the splitting is manged between upstream switch (normally a root complex on a mainboard) and the individual bifurcated devices. The splitting board itself is transparent in terms of PCIe negotiations and operations.
An old one for example was this
IO Crest card that had a bridge chip allowing all 4 drives to be seen by the OS even on mobos that don't support bifurcation (but that one is x16, and no idea if it can operate on x8 with reduced speed).
That card is in fact using a PCIe switch chip, which is the reason it works even when bifurcation isn't available on the mainboard. The mainboard still needs to support PCIe switches..
While bifurcation can only hard partition PCIe lanes, most of the time switches are used to multiplex/switch and over-subscribe PCIe lanes, so you would e.g. use them to put 4 NVMe drives into one 4x slot to increase capacity, but not bandwidth (IOPS could be better though).
They are much more expensive than bifurcation or even additional NVMe drives, so they have been very rare on DIY hardware, because all the distinct vendors were bought up by Marvell/Broadcom and prices went through the roof.
As active components they can also require quite a bit of power all for themselves with fans even for PCIe v3.
At PCIe v4 or v5 these switches become academically much more interesting, but unfotunately also 'unobtainium'.
Those were the ones I was thinking of (specifically, the few x8 options available out there), which could in theory help offset the x8 limitation while still allowing 4 or more M2 drives to show up (the few x8 PCIe 4.0 cards that support 4 NVMe).
The theoretical alternative I had in mind is something like a
Synology E10M20 x8 card in that can do 10GbE + 2 NVMe, leaving the other NVMe slots free for other adapters like you've mentioned.
In either case, taking your ideas into account, such add-in cards could theoretically offer even more expansion if any of the slots can present other adapters, allowing for multiple SATA SSDs or even some old-school high-capacity HDDs.
Now these specialty boards seem even more tempting to play around with.
Southbridges have mostly been rather rich multi-protocol switches allowing for a large degree of oversubscription and flexibility. NVMe/PCIe/M.2 has eliminated most of the overhead of protocol conversion (e.g. SATA or USB) but mostly by removing itself and turning to fixed lane allocations: it's "genious" oversell of what's essentially less functionality for more money.
AMD IODs and Intel PCHs are still really powerful switch chips, that one should be able to cascade almost to no limit, but they don't sell separately (and almost never as a separate add-in board) while getting just the PCIe switch part of that from another vendor will cost you an arm and a leg with plenty of compatibility nightmares on top.
IMHO it's a sitation that makes very little technical sense and is purely driven by vendor commercial interests.
Yes, it's tempting to play around with these specialty boards, but only until you look at their prices. Bifurcation hardware can easily cost 1TB of NVMe storage already, anything with a switch is almost cheaper to repurchase as a bigger NVMe drive...