The 12-sided coin was billed as “the most secure coin in the world” when it was introduced in 2017.
Its original designs featured the Northern Irish shamrock, Welsh leek, Scottish thistle and English rose.
But now the Crown dependencies, such as Jersey and overseas territories will be able to commission designs.
The Treasury, which oversees the Royal Mint (based in Llantrisant, south Wales) said the move would underline the close links between the UK and its territories.
Many of those territories have coins based on older versions of the £1 coin, which became increasingly vulnerable to sophisticated forgeries.
The newer coin’s security features include an image that works like a hologram, and micro-sized lettering inside both rims.
The government said its territories would now have the option to produce their own 12-sided coin using the cutting-edge technology to protect their cash.
It added that the new versions of the coin would be expected to feature images celebrating the heritage of the territories, with their history and culture pictured on the reverse side.
Crown dependencies of the UK are the Isle of Man, Jersey and Guernsey, while the UK overseas territories include the likes of the British Virgin Islands, the Cayman Islands, the Falklands and Gibraltar.
Lord Ahmad, the overseas territories minister, said: “As well as helping to boost their identity, these new coins will also bring increased security to each of these economies.”