We study the microphases of linear multiblock copolymers formed from monodisperse A- and B-type blocks in the limit in which the number of blocks is large. We find the lamellar, gyroid, hexagonal, and cubic microphases to be stable. Monocontinuous catenoid-lamellar and bicontinuous double-diamond phases are nearly stable in the region between the lamellar and hexagonal phases where the gyroid phase is stable. In the weak-segregation limit, the gyroid phase is not stable, and along the lamellar to hexagonal boundaries a bicontinuous catenoid-lamellar phase is close to stability. In the strong-segregation limit, we can examine only the lamellar phase, and we determine the scaling;behavior of its period and interfacial width. We conclude that multiblocks exhibit identical scaling exponents as diblocks.