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.