Originally Posted by Chris_W

It is certainly possible to put one larger cog behind a regular cassette, and remove an intermediate cog to get a wider-range cassette. It takes some playing around with different spacers between the loose big cog and the three on the carrier, but it certainly can be done. However, as mentioned above, I would not recommend doing so on a tandem because of the extra power that needs to be transmitted and the danger of damaging the freehub body.

I've done this on a single bike, where I made a custom 12-28 10-speed cassette. I took a 12-25 cassette, removed the 16 tooth, and used a loose 28 tooth on the back (which came from a partly-used 11-32 MTB 9-speed cassette), and used trial and error to find a couple of spacers that positioned the 28-tooth cog correctly in the end. This then gives me well-spaced low gears: 19-21-23-25-28. Interestingly, it appears that the 17 tooth cog was made to have a 16 tooth inside it, because shifting between the 15 and 17 is not quite as smooth as it should be, it sometimes require a little extra nudge which is not needed for any other shifts, but this is not a big deal. The 25-28 shift works fine. It would be great if someone were to start making a stock cassette like this.