Plate impact experiments are a powerful tool in equation of state development, but are inherently limited by the range of impact velocities accessible to the facility. In an effort to dramatically increase the range of pressures which can be studied with available impact velocities, a new experimental technique is examined. The target plate is replaced by a composite assembly consisting of two concentric cylinders. The target is designed such that the initial shock velocity in a well-characterized outer cylinder is higher than in the inner cylinder material of interest. Conically converging shocks will be generated at the interface due to the impedance mismatch between the two materials and axisymmetric geometry. Upon convergence, an irregular reflection occurs and the conical analog of a Mach reflection develops. This Mach reflection grows until it reaches a steady state, at which point the high pressure state in the Mach disk can be measured using velocity interferometry and impedance matching techniques. The technique is demonstrated by studying the shock response of copper. A strong confinement setup utilizes a low impedance 6061-T6 aluminum outer cylinder and the weak confinement case features a higher impedance molybdenum outer cylinder. The experimental results for copper are in good agreement with a simple analytical model, numerical simulations, and data in the literature. The possibility of utilizing full field measurements to make multiple Hugoniot measurements is also examined.