Base station antennas include a main module that has a first backplane that includes a first reflector. A vertically-extending array of first radiating elements is mounted to extend forwardly from the first reflector, and at least one first RF port is coupled to the vertically-extending array of first radiating elements. These antennas further include a sub-module that is attached to the first backplane. The sub-module includes a second backplane that has a second reflector that is separate from the first reflector. A vertically-extending array of second radiating elements is mounted to extend forwardly from the second reflector and is transversely spaced-apart from the vertically-extending array of first radiating elements. A plurality of second RF ports are coupled to the vertically-extending array of second radiating elements. The vertically-extending array of first radiating elements and the vertically-extending array of second radiating elements are configured to serve a common sector of a base station.