This study investigates the reflection of a moving shock on a stationary oblique shock – a prototype for supersonic vehicle encounters. Combining computational fluid dynamics (CFD) with a simplified model with key assumptions checked against CFD, we reveal how triple-point trajectories and pressure peaks evolve with wedge angle, and identify mechanisms governing transitions between interference types. It is shown that: (i) for Type V interference, the triple points move at distinct velocities, so the equations must be set in each triple point’s moving frame rather than in a single nominal intersection point’s frame of the incident and oblique shocks. Reducing the wedge angle weakens confinement, lowering overpressure and slowing triple-point motion. (ii) At the Type VI–V transition, a sudden Mach stem emergence creates a sharp pressure spike. (iii) For Type II and IV interferences, a major difficulty arises in determining the postreflection pressure behind the shock – a key to closing the model. This obstacle is overcome by treating the flow as a normal shock impinging on a wall, an analogy that yields the missing parameter and is checked by CFD. We also find that transitions between interference types are governed by the emergence and disappearance of triple points in their moving frames, accounting for deviations from classical critical conditions. These results uncover fine-scale flow physics previously overlooked in global studies.