  Recently, the so-called relative transverse activity classifier, $R_{\rm T}$,
has been proposed as a tool to disentangle the particle production originated
from the soft and hard QCD processes in proton-proton (pp) collisions. $R_{\rm
T}$ is a useful quantity to study particle production in events with
exceptionally large or small activity in the transverse region with respect to
the event-averaged mean. Contrary to the expectations, the preliminary results
of the ALICE Collaboration indicate that, e.g., the proton-to-pion ratio does
not exhibit the characteristic enhancement at intermediate $p_{\rm T}$ in
events with large $R_{\rm T}$ with respect to minimum-bias pp collisions. In
this work, we investigate the origin of this effect using the PYTHIA 8 and
HERWIG 7 Monte Carlo event generators. The effect is a consequence of a
selection bias attributed to wide-angle gluon emissions which creates jets that
populate the transverse region. Therefore, we propose a modified version of
$R_{\rm T}$ in order to suppress its sensitivity to hard gluon Bremsstrahlung,
and enhance the sensitivity to soft Multiparton Interactions (MPI). This
approach could be useful in order to study the particle production in the
jet-like region as a function of MPI. The implementation of these ideas in data
will provide more insight into the production mechanisms of hadrons in
high-multiplicity pp collisions, and its connection with heavy-ion phenomena.
