We investigate the impact of the $d^{*}(2380)$ hexaquark on the equation of state (EOS) of dense matter within hybrid stars (HSs) using the chiral mean-field model (CMF). The hexaquark is included as a new degree of freedom in the hadronic phase, and its influence on the deconfinement transition to quark matter is explored. We reparametrize the CMF model to ensure compatibility with recent astrophysical constraints, including the observation of massive pulsars and gravitational wave events. Our results show that the presence of $d^{*}$ significantly modifies the EOS, leading to a softening at high densities and a consequent reduction in the predicted maximum stellar masses. Furthermore, we examine the possibility of a first-order deconfinement phase transition within the context of the extended stability branch of slow stable HSs (SSHSs). We find that the presence of hexaquarks can delay the deconfinement phase transition and reduce the associated energy density gap, affecting the structure and stability of HSs. Our results suggest that, as the hexaquark appearance tends to destabilize stellar configurations, fine-tuning of model parameters is required to obtain both the presence of hexaquarks and quark deconfinement in these systems. In this scenario, the SSHS branch plays a crucial role in obtaining HSs with hexaquarks that satisfy current astrophysical constraints. Our work provides new insights into the role of exotic particles like $d^{*}$ in dense matter and the complex interplay between hadronic and quark degrees of freedom inside compact stellar objects.

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• Nuclear astrophysics
• Nuclear matter in neutron stars