The court on Friday ordered the secretary of state to submit a written response to the lawsuit, which was filed Thursday by the state Democratic Party.
The justices directed Democrats to submit additional written legal arguments and to outline what effect it would have in the election if the straight ticket option was allowed now that absentee voting has started in the general election.
The responses are due by Tuesday. The court hasn't decided yet whether to hold a hearing in the case.
Secretary of State Dianna Duran contends state law doesn't allow for voters to make a single mark on their ballots to support a party's entire slate of candidates.