There is an increasing demand for flexible, relatively inexpensive manufacturing techniques that can accommodate frequent changes to part design and production technologies, especially when limited batch sizes are required. Reconfigurable multi-point forming (MPF) is an advanced manufacturing technique which uses a reconfigurable die consisting of a set of moveable pins to shape sheet metal parts easily. This study investigates the use of a novel variable thickness waffle-type elastic cushion and a variable punch-loading profile to either eliminate or minimise defects associated with MPF, namely wrinkling, thickness variation, shape deviation, and dimpling. Finite element modelling (FEM), analysis of variance (ANOVA), and the response surface methodology (RSM) were used to investigate the effect of process parameters pertaining to the cushion dimensions and type of loading profile on the aforementioned defects. The results of this study indicate that the most significant process parameters were maximum cushion thickness, cushion cut-out base radius, and cushion cut-out profile radius. The type of loading profile was found to be insignificant in all responses, but further investigation is required as the rate, and the thermal effects were not considered in the material modelling. Optimal process parameters were found to be a maximum cushion thickness of 3.01 mm, cushion cut-out base radius of 2.37 mm, cushion cut-out profile radius of 10 mm, and a “linear” loading profile. This yielded 0.50 mm, 0.00515 mm, 0.425 mm for peak shape deviation, thickness variation, and wrinkling, respectively.