Calculating the Decay Rate for a Three-Body Decay

As the question states, how does one calculate the decay rate for a three-body decay $a rightarrow 1 +2 +3 $? For a two-body process, the answer is in the center-of-mass frame (Thomson, page 67, Eq. (3.22)): $$Gamma_{fi} = frac{p^{*}}{32pi^2m_a^2}int vert mathcal M_{fi} vert^2 dOmega,$$ but this formula doesn’t apply for a three-body decay, as far as I know, as $p_{1}^{*} = -p_{2}^{*}$ is set in the proof of this formula, since in a two-body decay, the daughter particles are produced back-to-back.