Can one prove Pareto efficiency in an n-party system by showing all Pareto improvements between any two given parties are made?
@HerrK. got it right in his comment (he should have deleted the somewhat confusing "yes" from the beginning and then posted it as an answer) It is possible that no pairwise improvements are possible but general Pareto-improvements are still possible. A simple counterexample for three actors and three goods is as follows. Let the utility functions be the same for all actors, that is
$$
U_A(x,y,z) = U_B(x,y,z) = U_C(x,y,z) = \min(x,y,z).
$$
Let actor $A$ have 3 units of good $x$, and 0 units of the other goods, whereas actor $B$ has 3 units of good $y$, and 0 units of the other goods, and actor $C$ has 3 units of good $z$, and 0 units of the other goods. No pairwise exchange can increase utilities above zero. But the goods could be distributed so that everyone has a unit of each. This would increase all utilities to one, making the original distribution not Pareto-efficient.