Two of the cases were set to go before U.S. District Judge Susan Bolton on Thursday.
Lawyers in separate cases filed by the federal government and by the American Civil Liberties Union and other advocacy groups are seeking an order to keep the law from taking effect.
Meanwhile, attorneys for Gov. Jan Brewer want Bolton to dismiss the lawsuit filed by the advocacy groups.
Bolton held a similar hearing on July 15 involving another lawsuit. She hasn't indicated whether she'll rule on any of the cases before July 29, when the law is scheduled to take effect at 12:01 a.m. MST.
The uncertainty has made the Sandra Day O'Connor U.S. Courthouse the focal point for the bubbling debate over the law, even as law enforcement agencies prepare to implement it and opponents gear up for protests.
The law requires officers, while enforcing other laws, to check a person's immigration status if there's a reasonable suspicion the person is in this country illegally.
The law does not define reasonable suspicion, but police training materials say triggers can include speaking poor English, traveling in a crowded vehicle and hanging out in an area where illegal immigrants typically congregate.