Products for food and feed derived from genetically modified (GM) crops are only allowed on the market when they are deemed to be safe for human health and the environment. The European Food Safety Authority (EFSA) performs safety assessment including a comparative approach: the compositional characteristics of a GM genotype are compared to those of reference genotypes that have a history of safe use. Statistical equivalence tests are used to carry out such a comparative assessment. These tests are univariate and therefore only consider one measured variable at a time. Phenotypic data, however, often comprise measurements on multiple variables that must be integrated to arrive at a single decision on acceptance in the regulatory process. The surge of modern molecular phenotyping platforms further challenges this integration, due to the large number of characteristics measured on the plants. This paper presents a new multivariate equivalence test that naturally extends a recently proposed univariate equivalence test and allows to assess equivalence across all variables simultaneously. The proposed test is illustrated on plant compositional data from a field study on maize grain and on untargeted metabolomic data of potato tubers, while its performance is assessed on simulated data.