We study the appearance of sexaquark (uuddss) as a candidate of dark matter in the core of neutron stars while there has been no experimental evidence of this particle in laboratories so far. Regarding the observational constraints of supermassive pulsars as well as gravitational waves, we encounter a sexaquark dilemma for which we introduce a solution by quark deconfinement fulfilling all present constraints from multi-messenger astronomy, i.e., tidal deformability in accordance with GW170817 and maximum mass above the lower limit from PSR J0740+6620.