  The separation of contributions from multi- and single-meson production in
the missing mass spectrum of the quasi-free pn --> pnX reaction constitutes
a~challenging task when the reaction is studied close to threshold. This is
especially true if the resolution of the mass determination is comparable with
the excess energy and if the investigated signal appears close to the
kinematical limit. In this article we outline a method which permits the
extraction of the signal originating from the creation of a single meson
without the necessity of conducting model-dependent simulations. For the pd -->
pnXp(spectator) reactions, the method allows one to combine events
corresponding to multi-meson production at various excess energies with respect
to the pn --> pn meson process, and hence leads to an increase of the
statistics needed for the determination of the shape of the multi-meson
background.
  As an example of the application of the method, we demonstrate that the
evaluation of the data from the pd --> pnXp(sp) process according to the
described technique enables one to extract a signal of the pn --> pn eta
reaction whose shape is consistent with expectations, supporting the
correctness and usefulness of the method introduced.
