The standard square grid has two axis: x and y, how would a grid made from tesselating equilateral triangles work? (An isometric grid) Triangles don't have 2 sets of parallel sides, like squares so as far as I can tell 3 axis are needed:
But then there is no easy way of interpreting it as each axis must have its respective grid lines coming of it from either a 30' angle or a 60' angle. And you have the problem where not all coordinate combinations can actually lie on the grid, eg. (x:1, y:2, z:3).
Is there some pre-existing method/standard of plotting "isometric coordinates" or is there no other way?

If you use just two of the axes on your diagram then you have an unambiguous set of coordinates for your system.