We consider the phase diagram of two randomly coupled Ising models to mimic the successive phase transitions in plastic crystals. Detailed mean-field calculations are performed. Depending on the strength of the couplings, the phase diagrams display three ordered phases and some multicritical points. A tetracritical point is found to turn bicritical as the strength of the couplings increases. The nature of this multicritical point is then analyzed by means of a momentum-space renormalization-group calculation. Using the replica trick, we obtain an effective n-component spin Hamiltonian. The random coupling is found to be relevant and shown to have drastic effects on the multicritical behavior. The lower critical dimension is estimated to be ${\mathit{d}}_{\mathit{l}}$=2. In the n=0 limit, to first order in the parameter \ensuremath{\epsilon}=4-d, a system of seven recursion relations is obtained. Although there is a stable fixed point, it cannot be reached from physically acceptable initial conditions. We give arguments to support a runaway of the flow lines associated with a fluctuation-induced first-order transition.