Coordinate transformations for systems of differential equations, the number of which $ \geq 3.$

Question

It is known that for systems of $2$ differential equations you can make transformations from Cartesian to polar coordinates, for example:

https://mathematica.stackexchange.com/questions/45339/polar-differential-equation

And what transformations exist for systems of differential equations, the number of which is equal to or exceeds $3?$