This paper describes the solution to a unique and challenging mixture experiment design problem involving: (1) 19 and 21 components for two different parts of the design, (2) many single-component and multi-component constraints, (3) augmentation of existing data, (4) a layered design developed in stages, and (5) a no-candidate-point optimal design approach. The problem involved studying the liquidus temperature of spinel crystals as a function of nuclear waste glass composition. The statistical objective was to develop an experimental design by augmenting existing glasses with new nonradioactive and radioactive glasses chosen to cover the designated nonradioactive and radioactive experimental regions. The existing 144 glasses were expressed as 19-component nonradioactive compositions and then augmented with 40 new nonradioactive glasses. These included 8 glasses on the outer layer of the region, 27 glasses on an inner layer, 2 replicate glasses at the centroid, and one replicate each of three existing glasses. Then, the 144 + 40 = 184 glasses were expressed as 21-component radioactive compositions and augmented with 5 radioactive glasses. A D-optimal design algorithm was used to select the new outer layer, inner layer, and radioactive glasses. Several statistical software packages can generate D-optimal experimental designs, but nearly all require a setmore » of candidate points (e.g., vertices) from which to select design points. The large number of components (19 or 21) and many constraints made it impossible to generate the huge number of vertices and other typical candidate points. JMP(R) was used to select design points without candidate points. JMP uses a coordinate-exchange algorithm modified for mixture experiments, which is discussed in the paper.« less