K-Nearest neighbor in transformed space
You can modify the matrix used to compute the distances between points. By default, KNN with quantitative features is used with Euclidean distances, this is, the identity matrix in the equation (x-y)' I (x-y) (it returns the squared Euclidean distance between point X and Y).

Instead of the identity matrix, you can use other positive definite matrices and compute Mahalanobis distances. 

Other modifications you can do is manipulate each feature. This also affects the output of KNN, aside of standardizing, you can try non linear modifications of the features, reducing kurtosis or skewness, for example.