  We introduce additional coalescence factors for the production of strange
baryons in a multiphase transport (AMPT) model in order to describe the
enhanced production of multistrange hadrons observed in Pb-Pb collisions at
$\rm \sqrt{s_{NN}}$ = 2.76 TeV at the Large hadron Collider (LHC) and Au+Au
collisions at $\rm \sqrt{s_{NN}}$ = 200 GeV at Relativistic Heavy-Ion Collider
(RHIC).This extended AMPT model is found to also give a reasonable description
of the multiplicity dependence of the strangeness enhancement observed in high
multiplicity events in $pp$ collisions at $\rm \sqrt{s}$ = 7 TeV and $p$-Pb
collisions at $\rm \sqrt{s_{NN}}$ = 5.02 TeV. We find that the coalescence
factors depend on the system size but not much on whether the system is
produced from A+A or p+A collisions. The extended AMPT model thus provides a
convenient way to model the mechanism underlying the observed strangeness
enhancement in collisions of both small and large systems at RHIC and LHC
energies.
