Laterally-arranged multiple bandgap (LAMB) solar cells based on InGaN nanowires or pillars with spatial composition-grading over a broad range over the surface of a single substrate were designed and simulated using Silvaco ATLAS software. The p-n junction is formed by n-type InGaN and a p-type GaP emitter, which is predicted to have a valence band well-aligned to In-rich InGaN based on a simple electron affinity band alignment model. Both three and six subcell designs were evaluated at various levels of solar concentration up to 240 suns. Efficiencies ranged from 32.9% to 40.2% for the three-subcell design and from 33.8% to 40.4% for the six-subcell design as the solar concentration was increased from one to 240 suns. A similar design utilizing a p-i-n structure rather than a simple p-n junction achieved 29.3% to 40.2% with three subcells and 36.1% to 46.2% with six subcells. The much greater benefit of increasing the number of subcells in the p-i-n design as compared to the p-n structure is attributed to more efficient carrier extraction, which enhances current-matching between subcells.