We can also coupled together four angular momenta. Consider two four-body states, with single-particle angular momenta $j_a$, $j_b$, $j_c$ and $j_d$ we can have a state with final $J$ $$|\Phi(a,b,c,d)\rangle_1 = | ([j_a\rightarrow j_b]J_{ab}\times [j_c\rightarrow j_d]J_{cd}) JM\rangle,$$ where we read the coupling order as $j_a$ couples with $j_b$ to given and intermediate angular momentum $J_{ab}$. Moreover, $j_c$ couples with $j_d$ to given and intermediate angular momentum $J_{cd}$. The two intermediate angular momenta $J_{ab}$ and $J_{cd}$ are in turn coupled to a final $J$. These operations involved three Clebsch-Gordan coefficients.

Alternatively, we could couple in the following order $$|\Phi(a,b,c,d)\rangle_2 = | ([j_a\rightarrow j_c]J_{ac}\times [j_b\rightarrow j_d]J_{bd}) JM\rangle,$$