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Recently, the so-called ``consistent thermodynamics'' of the LorentzianReissner-Nordstr\"{o}m (RN)-NUT-AdS$_4$ spacetimes has been pursued by a lot ofefforts via different means. Among these attempts, we had proposed a novel ideathat ``The NUT charge is a thermodynamical multihair" to successfully tacklewith the subject. In this paper, we will adopt this strategy to reconsider themass formulas of the RN-NUT-AdS$_4$ solutions but written in an alternativeform, which had not been studied before in any existing literature and might bea most appropriate ansatz for the higher dimensional multiply NUTty-charged AdSspacetimes without any constraint condition. Here, we shall discuss theChristodoulou-Ruffini-like squared mass formula and the first law as well asthe Bekenstein-Smarr mass formula by introducing the secondary hair $J_n = Mn$.For the sake of generality, we have introduced a dimensionless constant $w$into the constant factor $\Xi$ in the solution expression so that when $w = 1$,all obtained results can reproduce those delivered in our previous work.

Revisiting mass formulas of the four-dimensional Reissner-Nordstr\"{o}m-NUT-AdS solutions in a different metric form