I *may* have gone a little overboard.
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Special notes:
Acadian Piastre: Similar to New England, Acadia has its own shared currency, adopted in 1949. The Acadian Piastre does not have republican and monarchist variants for its currency; instead, Jerome Bonaparte is featured on the $5 note. Some commemorative coins do feature the current Prince of East Acadia on the obverse, but these are not in wide circulation.
Arques Pound: Arques no longer produces its own currency. From the beginning, higher-denomination notes were not produced in Arques to prevent sinful overspending; major purchases could be made through stacks of small bills or by going to the Mormon Church for special checks that were legal tender only in Arques. Beginning in the mid-20th century, Lower Louisiana Piastres became more common than Arques Pounds. The Arques Pound was discontinued in 1981.
Caribbean Pound: The governments of Bermuda, the Bahamas, and the Cayman Islands are currently in talks to establish a regional Caribbean Pound, expected to be implemented in the 2020s.
Carolina Reed (CLR): Originally called the Carolina Pound. In the early 19th century, the discovery of gold in Cabarrus County led to a massive gold rush. The largest mine was called Reed Mine, after its owner, and prospectors began referring to gold as "Reed nuggets." When the Carolina State Mint was founded nearby, it began to produce gold coins with the origin of the gold printed on the coin. Most of the coins were thus "Reed gold coins;" between "Reed nuggets" and "Reed coins," "Reed" became a common term for gold and money in Carolina, so the currency was officially renamed in the 1850s.
Christianan Krona (CRK): Christiania uses both the Swedish Krona and the Christianan Krona, which are not freely interchangeable; additionally, the significant Imperial Commonwealth population informally uses Commonwealth Rubles, which are pegged to the Krona at a rate of 7.1 rubles per Krona. This dizzyingly complex situation has led the Riksråd to propose ceasing production of Kronas and mandating the use of NND instead. The Krona features the Boreoamerican Turtle and the Pseudodemetrian Eagle side-by-side, the only ASB currency to do so.
New England Pound: The federation of New England has shared a currency since the late 19th century. Notably, each denomination has two variants: One depicting the current English Monarch, used within the Dominion, and one with one of New England's founding fathers, used in the republican states.
Poutaxian Pound: Poutaxia minted its own currency from 1821 to 1934. The economic depression of the 1930s led the Poutaxia congress to discontinue their Pound in favor of adopting the Pennsylvania Pound.
West Dominican Piastre: Locally known as the Gourde, though that is not its official name. The Piastre was originally pegged with the Lower Louisiana Piastre at 2 Dominican per Louisianan; when Lower Louisiana joined the standard currency regime, West Dominica joined as well by simply doubling the number printed on the old notes and bills. This has resulted in an idiosyncratic denomination regime that West Dominica has maintained, where among other things there are $4 notes but no $1 notes or coins.