PauliSigmaCombine[exp] is (nearly) the inverse operation
to PauliSigmaExpand.
SIS[p] + SIS[q]
PauliSigmaCombine[%]\bar{\sigma }\cdot \overline{p}+\bar{\sigma }\cdot \overline{q}
\bar{\sigma }\cdot \left(\overline{p}+\overline{q}\right)
PauliXi[-I] . (SIS[p1 + p2] + SIS[q]) . PauliEta[I]
PauliSigmaCombine[%]\xi ^{\dagger }.\left(\bar{\sigma }\cdot \left(\overline{\text{p1}}+\overline{\text{p2}}\right)+\bar{\sigma }\cdot \overline{q}\right).\eta
\xi ^{\dagger }.\left(\bar{\sigma }\cdot \left(\overline{\text{p1}}+\overline{\text{p2}}+\overline{q}\right)\right).\eta