Assume to tackle a particular group of instances for the integral multi-commodity flow problem.
Particularly, given a digraph $G = (V \cup S \cup T,E)$, such that $S, T, V$ are all disjoint. Furthermore, any $s_i \in S$ has only one exiting edge with capacity equal to its demand. Symmetrically, any $t_i \in T$ has only one entering edge, with capacity equal to its demand.
My question is, can I reduce the problem to a single-source, single-sink problem? My idea is to add a super-source and a super-sink with demand equals to the sum of original demands.
If this is feasible, I should be able to solve this particular group of instances in polynomial time.