  The motivation behind exploring jet quenching-like phenomena in small systems
arises from the experimental observation of heavy-ion-like behavior of particle
production in high-multiplicity proton-proton ($p+p$) collisions. Quantifying
the jet quenching in $p+p$ collisions is a challenging task, as the magnitude
of the nuclear modification factor ($R_{\rm AA}$ or $R_{\rm CP}$), which is
used to quantify jet quenching, is influenced by several factors, such as the
estimation of centrality and the scaling factor. The most common method of
centrality estimation employed by the ALICE collaboration is based on measuring
charged-particle multiplicity with the V0 detector situated at the forward
rapidity. This technique of centrality estimation makes the event sample biased
towards hard processes like multijet final states. This bias of the V0 detector
towards hard processes makes it difficult to study the jet quenching effect in
high-multiplicity $p+p$ collisions. In the present article, we propose to
explore the use of a new and robust event classifier, flattenicity which is
sensitive to both the multiple soft partonic interactions and hard processes.
The $\mathcal{P}_{\rm CP}$, a quantity analogous to $R_{\rm CP}$, has been
estimated for high-multiplicity $p+p$ collisions at $\sqrt{s} = 13$ TeV using
\texttt{PYTHIA8} model for both the V0M (the multiplicity classes selected
based on V0 detector acceptance) as well as flattenicity. The evolution of
$\mathcal{P}_{\rm CP}$ with $p_{\rm T}$ shows a heavy-ion-like effect for
flattencity which is attributed to the selection of softer transverse momentum
particles in high-multiplicity $p+p$ collisions.
