For improving the capabilities of general-purpose AI models and for extending their applicability to domains where the temporal dimension – among several others – is of importance, we will target the development of the next generation of Multimodal Space-Time Foundation Models (MSTFMs). These will combine spatio-temporal understanding, which is important even for modalities such as the visual one that have already been introduced in large generative models, with the effective management of new time-relevant modalities that are yet to be supported in foundation models, such as industrial time series data, remote sensing data and health-related measurements. Real and synthetic data, to mitigate data scarcity, will be leveraged for training general-purpose MSTFMs and for further adapting them for specific downstream tasks. Real data used for training will include data directly provided by members of the consortium as well as data from relevant European Data Spaces, while complementary synthetic data will be generated by exploiting existing generative AI capabilities as well as new ones developed in the project. European HPC infrastructure is directly included in the consortium to ensure the availability of the necessary computing resources.