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 ($pi/3<|phi^{rm trig.}-phi^{rm assoc.}|<2pi/3$) 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 ($3leq p_{rm T}^{rm assoc.}< 8$ 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.
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