  It is known that multiple partonic scatterings in high-energy proton-proton
($pp$) collisions must happen in parallel. However, a rigorous parallel
scattering formalism, taking energy sharing properly into account, fails to
reproduce factorization, which on the other hand is the basis of almost all
$pp$ event generators. In addition, binary scaling in nuclear scatterings is
badly violated. These problems are usually ``solved'' by simply not considering
strictly parallel scatterings, which is not a solution. I will report on new
ideas (leading to EPOS4), which allow recovering perfectly factorization, and
also binary scaling in $AA$ collisions, in a rigorous unbiased parallel
scattering formalism. In this new approach, dynamical saturation scales play a
crucial role, and this seems to be the missing piece needed to reconcile
parallel scattering with factorization. From a practical point of view, one can
compute within the EPOS4 framework parton distribution functions (EPOS PDFs)
and use them to compute inclusive $pp$ cross sections. So, for the first time,
one may compute inclusive jet production (for heavy or light flavors) at very
high transverse momentum ($p_{t}$) and at the same time in the same formalism
study flow effects at low $p_{t}$ in high-multiplicity $pp$ events, making
EPOS4 a full-scale ``general purpose event generator''. I discuss applications,
essentially multiplicity dependencies (of particle ratios, mean $p_{t}$, charm
production) which are very strongly affected by the saturation issues discussed
in this paper.
