  We analyze the behavior of cumulants of conserved charges in a subvolume of a
thermal system with exact global conservation laws by extending a recently
developed subensemble acceptance method (SAM) [V. Vovchenko et al.,
arXiv:2003.13905] to multiple conserved charges. Explicit expressions for all
diagonal and off-diagonal cumulants up to sixth order that relate them to the
grand canonical susceptibilities are obtained. The derivation is presented for
an arbitrary equation of state with an arbitrary number of different conserved
charges. The global conservation effects cancel out in any ratio of two second
order cumulants, in any ratio of two third order cumulants, as well as in a
ratio of strongly intensive measures $\Sigma$ and $\Delta$ involving any two
conserved charges, making all these quantities particularly suitable for
theory-to-experiment comparisons in heavy-ion collisions. We also show that the
same cancellation occurs in correlators of a conserved charge, like the
electric charge, with any non-conserved quantity such as net proton or net kaon
number. The main results of the SAM are illustrated in the framework of the
hadron resonance gas model. We also elucidate how net-proton and net-$\Lambda$
fluctuations are affected by conservation of electric charge and strangeness in
addition to baryon number.
