This paper discusses results from continued development of Inverted Metamorphic Multi-junction (IMM) solar cells with air mass zero (AM0) conversion efficiencies greater than 34%. An experimental best four-junction IMM (IMM4J) design is presented. In an effort to improve IMM performance in space radiation environments, 1-MeV electron irradiation studies are conducted on the individual IMM4J subcells. This data is used to engineer an IMM4J structure with beginning of life (BOL) AM0 conversion efficiency of approximately 34% and an end of life (EOL) remaining factor greater than 82%, where EOL is defined as performance after exposure to 1-MeV electron irradiation at 1E15 e/cm2 fluence. Next generation IMM designs are explored and an avenue toward AM0 conversion efficiencies of greater than 35% is presented.