According to Wikipedia, "At least thirteen original copies of the charter of 1215 were issued". These four are the only ones that survive.
The copy belonging to Lincoln Cathedral was sent in 1939 to be displayed at the World Fair in New York (and at the Library of Congress). After war broke out, Winston Churchill proposed that the document should be donated to the American people, as an enticement to join the hostilities on Britain's side; but the Cathedral opposed this plan, and it was dropped. Nevertheless the document did remain in the United States until after the end of the war (being kept at Fort Knox for much of the time). Since returning to Lincoln in 1946 it has been across the Atlantic and back on three further occasions, but it's currently on permanent loan to the David P. J. Ross vault at Lincoln Castle (sponsored by, and named after, the founder of Carphone Warehouse – who grew up in Lincoln and is now one of the richest men in Britain).
Other early (but not original) copies of the Magna Carta, which still survive, are one of the 1216 charter, which is held at Durham Cathedral, and four of the 1217 exemplification – one of which is at Hereford Cathedral, the other three in the Bodleian Library. There are also four copies from 1225: these are in Durham Cathedral, the British Library, the Bodleian Library, and the National Archives.
The next exemplification was made in 1297. Four copies of this version survive. One is held in the UK's National Archives, and one in the Guildhall, London – the ceremonial and administrative centre of the City of London and its Corporation.
The other two copies of the 1297 exemplification are the only two copies of the Magna Carta that are held outside England. One was bought by the Australian Government from King's School, Bruton, Somerset, in 1952, for £12,500 (probably equivalent to around £400,000 today), and is on display at the Parliament House in Canberra. The second was originally held by the Brudenell family, earls of Cardigan; they sold it to the Perot Foundation in the United States in 1984, and in 2007 it was bought by businessman David Rubenstein for $21.3 million. It's now on permanent loan to the US National Archives in Washington, DC.
A further version was made in 1300 by Edward I, and seven copies of this are known to survive. Six of them are held by the Town Council of Faversham, Kent, Oriel College in Oxford, the Bodleian Library, Durham Cathedral, Westminster Abbey, and the City of London. The seventh was discovered in 2015 in a Victorian scrapbook in the town archives of Sandwich, Kent (one of the Cinque Ports).
The Society of Antiquaries holds three copies: a draft of the 1215 charter (discovered in 2013 in a late 13th–century register from Peterborough Abbey), a copy of the 1225 third reissue (within an early 14th–century collection of statutes) and a "roll copy" of the 1225 reissue. I'm not sure what a roll copy is, but Culture24 (a support organisation for museums and "cultural professionals") describes this copy as "unique".
To summarise: I make that four copies from 1215, one from 1216, four each from 1217, 1225 and 1297, and seven from 1300. Total: 24. This does not include the three copies held by the Society of Antiquaries: one draft from 1215, one 14th–century copy of the 1225 version, and one "roll copy" of the 1225 version.
© Haydn Thompson 2021