  In 1932, Dirac proposed a formulation in terms of multi-time wave functions
as candidate for relativistic many-particle quantum mechanics. A well-known
consistency condition that is necessary for existence of solutions strongly
restricts the possible interaction types between the particles. It was
conjectured by Petrat and Tumulka that interactions described by multiplication
operators are generally excluded by this condition, and they gave a proof of
this claim for potentials without spin-coupling. Under smoothness assumptions
of possible solutions we show that there are potentials which are admissible,
give an explicit example, however, show that none of them fulfills the
physically desirable Poincar\'e invariance. We conclude that in this sense
Dirac's multi-time formalism does not allow to model interaction by
multiplication operators, and briefly point out several promising approaches to
interacting models one can instead pursue.
