An aircraft propulsion system includes a fan section that includes a fan shaft that is rotatable about a fan axis. The fan shaft includes a fan gear. The aircraft propulsion system also includes a boost turbine engine that includes a first output shaft that includes a first gear that is coupled to the fan gear. The boost turbine engine has a first maximum power capacity. The aircraft propulsion system further includes a cruise gas turbine engine that includes a second output shaft that includes a second gear that is coupled to the fan gear. The cruise turbine engine has a second maximum power capacity that is less than the first maximum power capacity of the boost turbine engine. The fan section produces a thrust that corresponds to power input through the fan gear from the boost turbine engine and the cruise turbine engine.