I can’t really provide specifics about what will/won’t fit, but I’d like to provide some context.
The Framework is a bit different from a typical laptop these days in terms of layout, so has different considerations that need to be accounted for.
Typical laptops, at least those the Framework is competing with in terms of general design/price/etc., these days have a panel on the bottom you remove to access RAM (sometimes one DIMM is under the bottom panel, the other is under a keyboard, but … I digress), storage, etc. So it’s possible to use thermal pads or other means to “thermally attach” the SSD to the bottom panel to provide a much larger heat sink that way.
However, the Framework has screws in the bottom that are holding the Input Panel (the keyboard, touch pad, power button) in place, and that input panel is removed to access the motherboard, RAM, storage, etc. This means that a thermal pad on the SSD would be thermally attaching the SSD to the keyboard, not the bottom panel. A drastic redesign would be required to use a thermal pad in the traditional sense.
That does mean that there may be more room for an SSD to have a heatsink, though. That said, the only limiting factor for a heatsink is NOT just the height available for said heatsink, but also air flow. For an SSD’s heatsink to perform well, it needs air moving over it to draw the heat it’s soaked from the NVRAM/controller away. Otherwise it’s just radiating the heat, a significantly slower process for cooling down. That might be fine for bursty loads but if actually needed for long, sustained read/write performance it won’t solve the problem and the SSD will thermal throttle. That’s a general issue in all PC’s, not just a Framework laptop.
Ultimately, while you may be able to fit an SSD with a larger heatsink into the Framework versus say a Dell XPS, the design of the Framework isn’t terribly conducive to such devices. I think a more typical NVMe, maybe with a “metal sticker” heatspreader like Samsung uses on a lot of their SSDs, is the best you can probably do.
The real question should be: Is it necessary? Many super high performance PCIe 4.0 NVMe SSDs do run incredibly hot when max’d out, but … do you require that in a Framework laptop? Most users, even among those of us that like the Framework for what it is/what it represents, aren’t doing such things. We’re more concerned with CPU, RAM, maybe GPU performance I imagine. NVMe performance is already well past what 95-99% of users “need” right now. I’m certain there are some users who would/could be running workloads that would be significantly more dependent on storage IO than say CPU, GPU, etc., but those workloads are not terribly typical, and for lack of a better phrase off the top of my head I’d call it a niche of a niche. So, beyond “check out these benchmarks, aren’t I a badass for having bought this thing?” numbers… you KNOW if you need a super high level of SSD performance. If you don’t know for sure you probably don’t need to worry about it. If you do, you’re going to look for the best possible performance NVMe you can fit in, you’re going to look at modifications, or you’re going to accept that the SSD will just thermal throttle sometimes. The rest of us: NVMe PCIe 3.0 SSD’s are almost certainly more than fast enough already, and using a “less performant” PCIe 4.0 SSD will still be just fine.
I personally went with an SK Hynix P31. More than enough performance for what I want, lower power usage that many of the competitors.
If you do require the absolute fastest SSD possible, I think the solution is simply figuring out what the maximum height from the PCB of the SSD is. Hopefully a Framework employee can provide that from a CAD or something since it’s hard to get a ruler into a closed laptop . Even with that, though, I can’t imagine the fan in the Framework is getting enough around the chassis to really help a dedicated SSD heatsink and instead… it might be better at thinking about a full cooler replacement that may include a vapor chamber and heatpipe over to the SSD slot? Maybe something for the Framework team to consider for a future Marketplace upgrade?