  This paper presents the production of charged particles associated with
high-$p_{\rm T}$ trigger particles ($8<p_{\rm T}^{\rm trig.}<15$ GeV/$c$) in
proton-proton collisions at $\sqrt{s}=5.02$ TeV simulated with PYTHIA 8.244.
The study is performed as a function of the relative transverse activity
classifier, $R_{\rm T}$, which is the relative charged-particle multiplicity in
the transverse region ($\pi/3<|\phi^{\rm trig.}-\phi^{\rm assoc.}|<2\pi/3$) of
the di-hadron correlations, and it is sensitive to the Multi-Parton
Interactions. The evolution of both the near and the away-side yield of
associated particles ($3\leq p_{\rm T}^{\rm assoc.}< 8$ GeV/$c$) as a function
of $R_{\rm T}$ is investigated. We propose a strategy which allows for the
modelling and subtraction of the underlying event contribution from the near
and the away side in challenging environments like those characterised by large
$R_{\rm T}$. We found that the away-side signal becomes broader with increasing
$R_{\rm T}$, while its corresponding yield is independent of $R_{\rm T}$.
Contrarily, the near-side yield increases with $R_{\rm T}$. This effect is
reminiscent of that seen in heavy-ion collisions, where an enhancement in the
near-side yield for 0-5% central Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$
TeV was reported. A discussion on the origin of these effects in PYTHIA, as
well as their implications for the interpretation of recent LHC results for pp
collisions, is presented.
