Abstract: Pure partition functions for multiple SLE are characterized by BPZ-type PDEs, M"obius covariance, and link-pattern asymptotics. In this talk I will discuss the first genuinely multivariable case, namely multiple $3$-SLE$_kappa$. After a M"obius-normalized change of variables, the problem reduces to trivariate power series in three unoriented cross-ratio variables. There are two basic topological types, the rainbow and neighbor patterns. I will explain how the reduced PDE system leads to coefficient recursions, how hidden symmetry is propagated through the coefficient lattice, and how the two-dimensional boundary degenerations are described by Appell $F_1$ and Horn $G_2$ functions. The rainbow case can be handled by direct coefficient estimates, while the neighbor case requires several Pfaff systems for analytic continuation and boundary control. Finally, I will describe how SLE martingales and It^o calculus enter the proof of positivity, and discuss the algebraic structure that appears at integer values of $beta=4/kappa$, including a conjectural formula in the neighbor case.