Nowadays, the Internet of Things and the e-Health are producing huge collections of Time Series that are analyzed in order to classify current status or to detect certain events, among others. In two-class problems, when the positive events to detect are infrequent, the gathered data lack balance. Even in unsupervised learning, this imbalance causes models to decrease their generalization capability. In order to solve such problem, Time Series balancing algorithms have been proposed. Time Series balancing algorithms have barely been studied; the different approaches make use of either a single bag of Time Series extracting some of them in order to generate a synthetic new one or ghost points in the distance space. These solutions are suitable when there is one only data source and they are univariate datasets. However, in the context of the Internet of Things, where multiple data sources are available, these approaches may not perform coherently. Besides, up to our knowledge there is not multiple datasources and multivariate TS balancing algorithms in the literature. In this research, we study two main concerns that should be considered when designing balancing Time Series algorithms: on the one hand, the TS balancing algorithms should deal with multiple multivariate data sources; on the other hand, the balancing algorithms should be shape preserving. A new algorithm is proposed for balancing multivariate Time Series datasets, as part of our work. A complete evaluation of the algorithm is performed dealing with two real-world multivariate Time Series datasets coming from the e-Health domain: one about epilepsy crisis identification and the other on fall detection. A thorough analysis of the performance is discussed, showing the advantages of considering the Time Series issues within the balancing algorithm.