In this work we present a generalisation of the Modified Kneser-Ney interpolative smoothing for richer smoothing via additional discount parameters. We provide mathematical underpinning for the estimator of the new discount parameters, and showcase the utility of our rich MKN language models on several European languages. We further explore the interdependency among the training data size, language model order, and number of discount parameters. Our empirical results illustrate that larger number of discount parameters, i) allows for better allocation of mass in the smoothing process, particularly on small data regime where statistical sparsity is sever, and ii) leads to significant reduction in perplexity, particularly for out-of-domain test sets which introduce higher ratio of out-of-vocabulary words.