The Fock-Hilbert space generated by a single-particle interaction-free Wightman field is augmented by introducing non-trivial multi-particle (that is, multi-point) field operators in a way that satisfies the Haag-Kastler axioms, which is justified insofar as Haag's theorem establishes that free field Fock-Hilbert spaces cannot model bound or interacting states. The 2-particle and 3-particle cases are special in 3+1-dimensions because a time-like 4-vector cannot be constructed that is orthogonal to more than three arbitrarily chosen space-like 4-vectors.