suggestion: Origami 500% 2x9
 

There are at least a few of us who would like to see a production folder with a 500% gear range, and the recently-announced Microshift Super Short drivetrain, designed for 20” wheels, makes it possible to achieve this with excellent ground clearance. It works with an 11-38 cassette, which one would need to combine with a front double. 36/52 would give 19”-95” gear range.
The capacity of the short tensioner would only allow the small ring to be used with the 3 largest sprockets; beyond that, the tensioner would be maxed out and the chain would start rattling against itself - a benign reminder to shift rings. The front rings should be mounted with the large one centred so that all 9 sprockets work with it (as in the intended 1x9 application), providing 27”-95”. The result is 11 real gears, with a 1-gear overlap and a low range that is a classic mountain granny, only used for steep hills.
For context, Sheldon Brown’s main ride back in the days of 5-sprocket clusters sported a 51/26 crankset with 29”-98” range and 10 real gears (no overlap) - called “alpine” gearing in those days. Recently, Russ of Path Less Pedaled has reverted to such a crankset, which he calls “wide-low” explaining in that he’s realized the extra range is worth it. (Commenters there mention centred large rings.)
As for current production folders, Tern offers 2x only on the 26” Eclipse line; 20” range maxes out at 420% (on a $2700 1x11). Dahon has an 11-speed Mu D11, but the cassette is only 11-32 - same as the Mu D8.
A few members here have built their own 500% drivetrains - which can turn out to be problematic even when mounts for a front derailleur are supposedly provided, leading to expedients such as having custom parts 3D printed.
So Origami could offer the greatest range on any 20” folder pretty easily, just by adding a front derailleur on a mount that really works to one of their existing frames.

If you want a bigger gear range, then you'd better consider a long cage rear derailleur.
Or you can think about IGH systems. For example, the SRAM DD3 hub with a 11-28cassette can already provide you a 500%+ range

You can get ~700% range with a Sturmey-Archer CS-RK3 with a 42 tooth chainring & an 11-42 tooth cassette. I have such a setup on a 700c gravel bike. Way more is possible so long as you mind the 1:1 low/low drive ratio.

A Haberstock Mobility Schlumpf drive is another option. I have the Speed-drive (1.65) mated to a Nexus 7. 400% range.

A (2.5) High-speed drive would yield 575% Even greater range could be realized if the HSD was mated to an Alfine 8...Around 720% Though, I don't know how often 90rpm at 35mph on a folder would be practical.

Hmph. Is this stated in Sturmey's literature somewhere?

Yes.
They state it as something to the effect of: "Max cog is 34 tooth." & combine it with: "Road, not mountain."

Ergo: As sub-compact road cranksets are 50-34, the lowest drive ratio is 1:1. It's not hard to see the engineers at Sturmey don't feel that people understand what a drive ratio is, what it means, or how to arrive at one. The gamble is drive ratios are too complicated for Joe consumer. Joe consumer wants a concrete number. That number in this case is 34.

There is probably a sizable safety margin as some road cranksets came in the triple variety & anecdotal evidence from an online review in a popular mountain bike website, whereby a spokesperson from the design team suggests that (& I quote): "You're not gonna hurt it" to the reviewers. The reviewers hammered it & it came out fine. You can do the leg work. It's not hard to type "CS-RK3 reviews" into your favorite sort engine.

Bounce the Sturmey 3 speed at gear-calculator . com and see at what drive ratio it kicks out a high torque warning. (You'll see it's 1:1)

...maybe the TS want the lightness and efficiency of external gearing. I can't see how 500% could be a problem with 2x9, even with a 16" folder. Unless you really want to be able to drive biggest rear cog with the big chain ring and smallest cog with small chain ring, then you need a MTB derailleur.

I am not a fan of front derailleurs, but I do see the benefit of a wider gear range. I would never install a drivetrain that would max out the tensioner in any configuration because it would be a PR nightmare. I am not interested in fielding those calls.

I am always interested in making improvements where we can, and within reason. A Rolloff IGH can give us a 500+% range, but at a steep cost.

Our upcoming Scorpion folding recumbent (the world's most compact production folding recumbent) utilizes an 11-40 10-speed gear set out back with a Shimano Tiagra RD-4700, and a 39-52 out front for a 488% range (18 to 88 gear inches). So, we could duplicate this setup on any of bikes if there were sufficient demand.

@GTA & base2: as splithub mentions, efficiency losses compound in a derailleur / IGH hybrid, and a front derailleur is also lighter and cheaper. Hard to see why a system which is heavier, more expensive and less efficient should be preferred. As for long-cage derailleurs - you're skimming pretty close to the ground there with a 20" wheel. I have a medium cage to reach 300% range, and already have to be careful around curbs.
@Pinigis: as the inventor of the Flybar super-pogo, I hear you about the constraints of anticipated misuse, and won't argue with your decision. However I'll mention that you would still offer the only non-onerous, off-the-shelf route to 500% if you equipped a bike with a tested FD mount and bolt holes for a granny ring. It wouldn't matter to many, but it wouldn't cost much either. If that bike also came with outstanding ground clearance from the supershort RD, so much the better.

While agree with what you're saying to an extent, but the reason is that with 3-speed IGH the steps can be greater than with a derailleur. So, you don't end up with redundant gears. You get nice even steps all the way through. And with a 3-speed IGH the weight and efficiency differences are small. So for small wheeled bikes where longer cages are problematic, this is one solution. That said, I tend to favor derailleur 1X's, but I live in flatlandia..

Antifriction because in a hybrid drivetrain with a Schlumpf, DD3, or CS-RK3 the wrap is the same as an a 1x. In a Schlumpf/IGH system the wrap is 0.

An equivalent wrap for such a wide range in a straight derailleur system would be nigh impossibly large even with out ground clearance constraints.

A Schlumpf HSD/Alfine 8 is 220% more range than your suggestion & has zero wrap to speak of. It completely takes derailleur cage length & ground clearance out of the equation.

An additional 1-2% loss in running efficiency in exchange for a robust, durable, compact system that is not subject to the same wear, maintenance, or abuses as conventional systems, to some, is considered worth the trade off. Thats why.

The range % capability of such systems discussed here border on the limit of practicality for all but the most niche end use case. Joe consumer going to the bike shop to buy transport to/from the bus stop just doesn't present a viable use case for a system of this design.

I think it would be best to leave the bike design to the bike designers...Just because you can do a thing doesn't mean it makes smart business sense or that Joe Consumer will even understand what "% range" even means even if given proper context.