I'm not sure you'd ever be able to take it to a 6-speed. But maybe a 12-speed is possible.
I asked the question a while back after a mate of mine got his 4-speed.
This is the thread:
https://www.cyclechat.net/threads/adding-an-extra-gear-to-a-4-speed.290120/
But in the meantime, the 12-speed bike has launched which is a 4-speed derailleur and a 3-speed hub.
I don't know enough about them to know if it's a simple wheel swap and additional cabling. Something in the back of my mind has me thinking the 12-speed has a wider triangle, but not sure.
Weirdly, the 3-speed bike has a wider range - which would cure one of your problems - but make the other problem worse (the gaps between the gears). In fact I think one of the selling points of the 4-speed is the fact that the ratios are quite close.
Here's how the various bikes stack up.
Also, from
another forum, someone emailed Brompton and got the following reply:
Thank you for contacting us here at the Brompton factory and for your interest in our bicycles.
Yes, you may upgrade your current 4-speed gear P line to 12-speed. However, the upgrade might be costly. Below there is the list of what parts customers will need to perform the upgrade based on the model they own:
- 12 Speed Hub Gear Indicator Chain
- Hub Gear Cbl Pulley Ass Rr
- Hub Gear Cbl Anchorage Sturmey
- Hub Gear Shift Set with LH Brake
- Superlight 12 Spd Brom Rear Wheel - Ryde
- Rear wheel hub guide nut
Gear cable depending on HB type
- H Type hub gear cable
- M Type hub gear cable
- S Type hub gear cable