A new approach for engineering a variety of unconventional laser beams with complex spatio-temporal characteristics using coherent (coherently combinable) fiber-array laser transmitter systems is proposed and analyzed through numerical simulations. These laser beams, referred to here as exotic beams, include beams with periodic, quasi-periodic, and stochastic spatio-temporal phase modulation. We show that exotic laser beams can be generated in fiber arrays using feedback control systems of different architectures based on a network of beam-tail interference sensors and fiber-integrated phase shifters. Due to the extremely short (nanosecond time scale) response time of these phase shifting elements, the proposed technique permits generation of laser beams with controllable spatial coherence which can be used for mitigation of speckle effects in various applications including directed energy, laser communications, active imaging, and wavefront sensing. Results of analyses and computer simulations of exotic beams are presented for the fiber-array system with seven subapertures.