  We study rapidly spinning compact stars with equations of state featuring a
first order phase transition between strongly coupled nuclear matter and
deconfined quark matter by employing the gauge/gravity duality. We consider a
family of models, which allow purely hadronic uniformly rotating stars with
masses up to approximately $2.9\, \mathrm{M}_\odot$, and are therefore
compatible with the interpretation that the secondary component
($2.59^{+0.08}_{-0.09}\, \mathrm{M}_\odot$) in GW190814 is a neutron star.
These stars have central densities several times the nuclear saturation density
so that strong coupling and non-perturbative effects become crucial. We
construct models where the maximal mass of static (rotating) stars
$M_{\mathrm{TOV}}$ ($M_{\mathrm{max}}$) is either determined by the secular
instability or a phase transition induced collapse. We find largest values for
$M_{\mathrm{max}}/M_{\mathrm{TOV}}$ in cases where the phase transition
determines $M_{\mathrm{max}}$, which shifts our fit result to
$M_{\mathrm{max}}/M_{\mathrm{TOV}} = 1.227^{+0.031}_{-0.016}$, a value slightly
above the Breu-Rezzolla bound $1.203^{+0.022}_{-0.022}$ inferred from models
without phase transition.
