We propose the remote multiplexing of holograms with random patterns from a multimode fiber bundle used as the reference beams. The random pattern reference beam is characterized by the superposition and concatenation of propagation modes of multimode fiber and free space. For angle, shift, and wavelength remote multiplexing we compare two methods of laser coupling to the fiber bundle, i.e., direct coupling and lens coupling. A theoretical discussion that uses mode orthogonality is provided to describe multiplexing characteristics, and the theory is verified by experimental results. These remote-multiplexing methods can be applied to general multimode waveguide arrays for construction of compact and integrated optical systems in which multiplexing can be controlled remotely.