The Large Eddy Simulation (LES) mean data of a flow past a splitter plate is analyzed using resolvent analysis with the objective of motivating a passive control strategy. The configuration of interest consists of two streams; a supersonic (Mach 1.23) upper stream and a sonic (Mach 1) lower stream, separated by a splitter plate of non-negligible thickness. Canonically, these two streams and the plate represent the supersonic multi-stream nozzle flow in an airframeintegrated variable-cycle engine architecture, with the upper stream being analogous to the power-producing core stream, and the lower stream being analogous to the bypass stream which shields the airframe from the thermal and acoustic loading of the core while providing some other design benefits. Numerical and experimental campaigns in previous studies have shown that this flow characteristically exhibits a two-dimensional vortex-shedding-like instability, which has a potentially detrimental first-order impact on performance. To gain insight into the instability mechanism, resolvent analysis is used to obtain the spatial structure of the optimal forcing of the mean flow. Modifications to the trailing edge of the plate, in the form of sinusoidal spanwise crests and troughs, are then introduced to interfere with this internal forcing mechanism and the resulting flows are simulated with LES. Proper Orthogonal Decomposition (POD) using snapshots of the LES data along the streamwise direction reveal a substantial increase in the rank of the modified flow, with a diminishing of the shedding instability as the spanwise wavenumber of the trailing-edge features is increased. Additionally, Dynamic Mode Decomposition (DMD) results reveal that the trailing-edge features induce a superposition of several resolvent response modes which rapidly decay downstream due to the non-linear action of turbulence.