We present an extension of a previous work where, assuming a simple free bosonic gas supplemented with a relativistic meand field model to describe the pure nucleonic part of the EoS, we studied the consequences that the first non-trivial hexaquark $d^*$(2380) could have on the properties of neutron stars. Compared to that exploratory work we employ a standard non-linear Walecka model including additional terms that describe the interaction of the $d^*(2380)$ di-baryon with the other particles of the system through the exchange of $sigma$- and $omega$-meson fields. Our results have show that the presence of the $d^*(2380)$ leads to maximum masses compatible with the recent observations of $sim 2$M$_odot$ millisecond pulsars if the interaction of the $d^*(2380)$ is slightly repulsive or the $d^*(2380)$ does not interacts at all. An attractive interaction makes the equation of state too soft to be able to support a $2$M$_odot$ neutron star whereas an extremely repulsive one induces the collapse of the neutron star into a black hole as soon as the $d^*(2380)$ appears.
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