Multi-mode systems, like cavities, fibers, etc, often suffer from the presence of environmental noise which causes mode mixing and subsequent interference between various modes. In many occasions, the study of the exact wave dynamics is a formidable task, due to the many degrees of freedom that have to be taken into account in the equations of motion that describe such systems. Instead, a statistical theory of wave propagation might be a best way to describe the wave transport in such frameworks. Following this way of thinking, we have utilized a Random Matrix Theory modeling which allows us to study the spreading of an initial mode excitation in the mode-space due to the environmental noise. Using this method, we have developed a systematic approach that enforces a variety of wave spreading scenarios mimicking generalized Levy-type dynamics that it is imposed from engineered noise correlations. Our theoretical predictions have been tested in realistic circumstances, like in paraxial light propagation in multimode fibers with tailored fiber cross-section modulations or in micro-cavities with time-modulated boundaries.