I would like to extend the range of a 6-speed Brompton with 12% lower gearing. I am happy with the lower end of the range, handy for the hills I need to tackle, but I find the upper end is not enough when I am on the flat areas. Could the cog for the higher gears be changed into something that would give me what I want? I am not too worried about having a range of gears with a large gap in the middle.

Thanks

I've Got a front derailleur bracket I got from CM Wasson to sell or return,
then you have a 3rd lever, a thumbshifter.
procrastinating on returning it .. as the Mountain drive works better for me.
sell for what he charged me for this custom made powder coated bracket
to mount a Braze-on type front derailleur .

common crank used, a 53/39, or perhaps a 52/42.. PM to chat..

Brompton says the 13/15 on the hub gets the job done best on that end , half step..

You could also buy a Schlumpf Overdrive planetary 2 speed crankset aka
speed drive 1.65% X, or high speed drive 2.6X

Thanks for the offer, but I am after a solution that doesn't involve a 3rd lever, unhappy enough with having two.

Mountain/speed drive cranks shift with a button you tap with your heel. no added lever.

it's in the place where the crank arm fits onto the spindle.

https://schlumpf.ch/antriebe_engl.htm

https://kinetics.org.uk/html/mountain_drive.shtml or https://www.foldabikes.com/

I got a Mountain drive for My Brompton 54t + a 15t on my AW3 hub,

in low the crank is in effect a 21.6t [it's hilly and then some, here]

Yes it can. Search the threads for a 12/17 or 12/18 cog combination.

FWIW,
Mk3 sram 3x2 hubs are 3 speed spline Mk4 sturmey BWR hubs are shimano spline

on My Older Mk 2 bike rear end 15t is as large as fits , before the frame tube interference hits it.
I have a 15t cog from the Sram hybrid hub on my sturmey AW3.

Thanks for the warning. I have an SRAM 3 speed.

So it seems I need to get a custom made cog, but the one I am interested in changing is the smaller one, so might be hard to go smaller than what I have, which is a 13. Maybe a larger chainring combined with a larger large cog to compensate?

So, another possibility, is get regular sturmey cogs ground thinner, to take 3/32 chain, as they make 1/8" thick to 22t.

Highpath Engineering, In Wales UK, has made some larger cogs of aluminum to fit in these situations , before , [seen pictures] and as they are set up to make custom chainrings for any user, they may do so again.

Ive been pretty happy with My Mountain drive kit, a 13/15 set on the hub would narrow the spacing and double the ratios.
so there would be 12 vs the nicely practical 6 , there is no overlap of any ratios, the 3<>4 gap is only slightly wider than the 1,2,3 at 33%, its 41% as i recall .. on Sheldon's Gears calculator site ..

I have the stock Stronglight made 50t crankset in a box now , that I took off..
if you have your bike fitted with the 44.

Fit a BWR hub to widen the range. Changing one of the two cogs will mess up the relatively even interlaced gear pattern.