What is the maximum tooth sprocket you could fit on the back using a Deore DX rear derailleur?

[retrobiker273891]

2/3+2/3 is not as long as a hanger with an extender added. But using an Xacto hobby saw you can cut opposite ends off of 2 hangers and make a longer one. The DIY idea looks good except a lot of hangers are thinner in some places, which is a little harder to DIY.
But yes 40t with just a longer B screw.
Here it is in action (my video skills suck)
50tx11-40t 8 speed cassette with Rapid Rise XTR mid cage, RR Revoshifter, and zip tied cassette to activate the front freewheel in the motor.

2004 Gary Fisher Solstice comfort bike with lots of MTB rated upgrades + the motor.
There are reports of Shimano Zee M640 short cage derailleurs doing this also. You need the Freeride version, not the DH model.
The shift ratio ended up the same as SRAM 1:1 so 8/9 speed with SRAM shifters is on the menu also. This means 9 speed twist shifters can be used. Clutch type deraillleur with no plastic bits if you want to update an older bike. SRAM 11 speed gipshifter work with these and the SLX mid cage also.
I have the mid cage SLX on my XC bike with SRAM 11s gripshifter. I own the Zee but might ship it off to my brother in NYC for stress testing. Keeping the derailleur out of the spokes is more of an issue for him.

The video didn't show anything regarding the 2/3+2/3 hanger. Still don't understand what that is tbh.

 

[bold stelvis]

Just buying an extension is the sensible choice if you really want to try this
as others have pointed out it might compromise shifting, especially at the high end of the gear range (ie the smallest sprockets) as its essentially just pushing the derailleur further away from the sprockets

It potentially has a negative effect on capacity as well - most people trying this sort of thing tend to be on 1 x setups up front, not a triple with a very small granny ring!

that doesn't mean it definitely won't work, just things to be mindful of if you're determined to try.

they are not expensive and likely to be accurately made as opposed to a DIY bodge if you're not entirely sure what your up to (which I'm pretty sure applies)

ZTTO Derailleur Hanger Extender

Fits to your current derailleur hanger to extend the hanger further allowing use of much larger cassettes. In some cases this means you can use a short cage derailleur on a 11-40t cassette! Perfect for a single chainring set up on a gravel/cx/adventure bike.

www.sjscycles.co.uk

Sonder Spur Derailleur hanger extension

Derailleur hanger extension to run wider gear ranges with your road bike mech. Perfect for riders who simply want to run a bigger cassette to get lower gearing.

alpkit.com