The study by kinetic mean-field techniques of a d-dimensional Ising system characterized by a sort of dynamical disorder reveals a rich phase diagram which exhibits a non-equilibrium tricritical point (only) for d>2, and re-entrance phenomena. The system time evolution is stochastic due to the simultaneous action of several independent spin-flip mechanisms, each corresponding to a different applied magnetic field. Such competition brings about randomness and a type of frustration that may occur also in real systems. In fact, this models the actual case of a magnetic system under a very rapidly fluctuating field, for example. Furthermore, the system may be interpreted as a non-equilibrium random-field system which, unlike the familiar quenched and annealed cases, contains a fast random diffusion of disorder.