Oh,Modern day?
That would be impossible wtihout some alien space bats giving them gatling guns
I'm interested in what is possible,Before they eventually decline adn collapse.
How about, not Alien Space Bats, but their Suzerain the Empress of India gives them these gatling guns?
That is: the 19th century Englishmen find, say, Kashmir Valley and the surrounding Himalayas occupied by a state whose elite speaks a language which is as recognizably Greek as the language spoken by 19th century Osman subjects being Greeks (but as different from the Osman Greek as Osman Greek is from spoken 3rd century BC Koine), and writes a language very different from the language they speak (just like the Osman subjects do - and the language Kashmir Greeks write is the same koine written by 19th century Osman Greek elites and read and taught in 19th century English schools). And that elite, unlike the 19th century Osman Greeks, have never been Christians - a large part of their religious practice is honestly worshipping the gods in temples which are as recognizable to the English readers of Greeks, as the churches used by 19th century Orthodox Greeks are recognizable by the scriptures and buildings of 1st or 4th century Christians.
A significant part of these Greek speakers also worship Gautama Buddha and worship him by making new Gandhara style images. And the state also includes subjects who speak Indian languages and worship Hindu gods.
And even though Muslim states have occasionally attacked Kashmir Greeks in last centuries, and sometimes extracted submission, they have never managed to establish direct control, and Muslims are no more than a small minority of urban immigrants.
So... how would the 19th century British Raj interact with this type of Greco-Indian kingdom?
Would they want to hire Greek mercenaries as a "martial race" along with Gurkhas?