The three-dimensional interactions of shock structures and multiple shear layers in a two-stream exhaust produced by a three-stream engine are documented. This paper focuses on the near-field pressure generated by Large Eddy Simulation (LES) and is based on pressure in two perpendicular sections and four transverse sections. After a basic documentation of the sound pressure level (SPL) and power spectra, we identify hot-spots (regions of large pressure fluctuations) as structures participating in the dynamics of the complex 3D flow. Cross-correlations between the hot spots and the entire pressure field reveals the propagation of fluctuations and possible interactions and acoustic waves in the jet. The interactions between the shock structures and shear layers are also studied in specific frequency bands, which enable us to map out some of the communication pathways between the flow structures.