multiReesIdeal(..., BasisElementLimit => X)
mixedMultiplicity(..., BasisElementLimit => X)
mixedVolume(..., BasisElementLimit => X)
secMilnorNumbers(..., BasisElementLimit => X)
Here X is a positive integer. Each of these functions computes the Rees ideal using 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.