Rigorous privacy-preserving mechanisms that can process and analyze dynamic data streams in real time are required to encourage a wider adoption of many large-scale monitoring and control systems recording the detailed activities of their users, such as intelligent transportation systems, smart grids, or smart buildings. Motivated by scenarios where signals originate from many sensors capturing privacy-sensitive events about individuals and several statistics of interest need to be continuously published in real time, we consider the problem of designing multi-input multi-output (MIMO) systems processing event streams, while providing certain differential privacy guarantees on the input signals. We show how to construct and optimize MIMO extensions of the zero-forcing mechanism, which we previously proposed for single-input single-output systems. Some of these extensions can take a statistical model of the input signals into account. We illustrate our privacy-preserving filter design methodology in two examples: privately monitoring and forecasting occupancy in a building equipped with multiple motion detection sensors, and analyzing the activity of a Markov chain model of a simple shared processing server.