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The maximum mass of neutron stars ($M_{\rm TOV}$) plays a crucial role inunderstanding their equation of state (EoS). Previous studies have used themeasurements for the compactness of massive pulsars and the tidal deformabilityof neutron stars in binary neutron star (BNS) mergers to constrain the EoS andthus the $M_{\rm TOV}$. The discovery of the most massive pulsar, PSRJ0952-0607, with a mass $\sim 2.35M_{\odot}$, has provided a valuable lowerlimit for $M_{\rm TOV}$. Another efficient method to constrain $M_{\rm TOV}$ isby examining the type of central remnant formed after a BNS merger.Gravitational wave (GW) data can provide the total mass of the system, whileaccompanying electromagnetic signals can help infer the remnant type. In thisstudy, we combine all the previous constraints and utilize the observationalfacts that about $24\%$ of the short gamma-ray bursts are followed by an X-rayinternal plateau, which indicate that roughly this fraction of BNS mergersyield supermassive neutron stars, to perform (Markov Chain) Monte Carlosimulations. These simulations allow us to explore the probability densitydistribution of $M_{\rm TOV}$ and other parameters related to BNS mergers. Ourfindings suggest that $M_{\rm TOV}$ is likely around $2.49M_{\odot} -2.52M_{\odot}$, with an uncertainty range of approximately [$-0.16M_{\odot}$,$0.15M_{\odot}$] ([$-0.28M_{\odot}$, $0.26M_{\odot}$]) at $1\sigma$ ($2\sigma$)confidence level. Furthermore, we examine the type of merger remnants inspecific events like GW170817 and GW190425 to further constrain $M_{\rm TOV}$and other relevant parameters, which can help to understand the physicalprocesses involved in BNS mergers.

What constraints can one pose on the maximum mass of neutron stars from multi-messenger observations?