  We start by defining two-particle operators that appear in celestial CFT. We
then show how to compute their OPE coefficients with the known single-particle
operators at tree level from multiparticle factorization channels, focusing on
the leading contribution involving the two-particle states. These factorization
channels only give us single-particle exchanges. To extract the multiparticle
exchanges, we look at the $\overline{\rm MHV}$ gluon amplitudes and show how
non-factorization channels contribute to two-particle terms in the
single-helicity sector. This is a first step towards systematically computing
the full celestial OPE.
