multiReesIdeal(..., PairLimit => X)mixedMultiplicity(..., PairLimit => X)mixedVolume(..., PairLimit => X)secMilnorNumbers(..., PairLimit => X)Here X is a positive integer. The calculation of Rees ideal requires a saturation step, and the optional argument causes the saturation process to stop after that number of s-pairs is found. This is described in the documentation node for saturate.