Two cogs on coaster hub?
 

I know it's not uncommon on old SA hubs for people to replace the 1/2" cog with a pair of dished 3/32" cogs and adding a derailleur for stepped gearing. Is this possible on a regular coaster brake hub running a standard 1/2" cog?

Also, is there any reason I'd have trouble shifting between a really small and a really big cog, i.e. 23t and 15t?

Just did this topic this week before.... but for a freewheel 3 speed ..

There would be a possibility of using a second chainring also,
same number of teeth, smaller that the rear, is larger .

so when you stop, pull out your wrench, loosen the nuts,
and shift the chain over from one pair of sprockets to the other pair,
the chain length would be the, appropriate, same for both.

As I recall the standard answer is as follows

Yes, it's possible to fit two cogs onto a SA hub, and with a three speed, you can get six speeds. However, a coaster brake drive train cannot use a sprung chain tensioner, you would have to change gears manually, by loosening the wheel and manually derailing the chain when stopped, in much the same way one might use a Dingle cog.

I'm not quite sure why you would want to build up a bike like that, but I think it could be done.

I forgot about that. Backpedalling just twists the derailleur once the brake is engaged, which is also why you can't use a chain tensioner with a fixie hub. Stepped gearing with manual adjustment is an interesting thought, but obviously there's no way to fit a quick release and it would be somewhat limited in range (i.e. dropout adjustment between a large and small cog.)

You can get over the movement of the axle by using two chainrings and two cogs. As long as the tooth difference between the chainrings is equal to the tooth difference in the cogs, the overall position of the axle remains the same. You can get some widely varied gear ratios like that.