While playing a game of Civilization 6 I would like to increase the difficulty level after playing a few hundred turns. Is this possible?
No. Part of the difficulty in this and other strategy games usually comes from starting bonuses the AI receive so it would not be a straightforward switch if you could.
The details of the difficulty settings can be found here. https://civ6.gamepedia.com/Game_difficulty
There may be a way to hack the save file but this of course would not undo the bonuses they have had to this point.