Okay, disregarding the unit of measurement (pounds, dollars, yen, whatnot) take a slug of given size and produce fractional monetary values by producing wedges of a size proportional to the value of the wedge. So a half dollar/pound/whatnot is half a circle, a quarter unit is a quarter circle, etc.
Very pieces of eight and all that.

Now make the pieces interlocking, so one can produce a coin of any given value below the whole unit (unlike concentric coins). Individual values are easy to determine for the sightless and slugs of different diameter or thickness can be used for different base values ($1 slug, $10 slug, $100 slug, etc). The individual pieces pose less of a choking hazard to children, too (though there _is_ a stabbing issue to contend with).

Coin-operated machines would have to be retrofitted, but the upshot is that a coin of a given value will always be a certain percentage of the whole; regardless of how it's assembled.

Individual wedges could be constructed of different materials or made otherwise visually distinctive, though that's not required.

You could overcome the stabbing issue by rounding off the ends.

How about issuing slightly twisted coins, so that they assemble into a close-fitting helix. So, if I had £2.20, I could snap the coins together to form a helix of 2-and-a-fifth revolutions.