The article compares multiple distributions using a new test based on kernel mean embeddings. This method can handle complex data and allows for an increasing number of distributions as the sample size grows. The test statistic converges to a Gumbel distribution, but with too many parameters to be practical. To solve this, the test is implemented using permutations and is shown to be effective against certain types of differences between distributions. An inequality for the permuted test statistic is also developed during the analysis.