A plan approved by the Texas Senate would cap the number of high-ranking high-school seniors who must be promised a spot at the state university of their choice, in what could be the most significant change in the state’s guaranteed-admissions law since it was enacted a decade ago.

Under the measure, which passed on Friday, 28 to 2, universities would be required to fill up no more than 60 percent of their freshman classes with students who ranked in the top 10 percent of their high-school graduating classes, the Dallas Morning News reported.

In recent years, more than 70 percent of freshmen at the University of Texas at Austin have been admitted based solely on class rank. Officials there say the 10-percent law, which was enacted in 1997 after a federal court struck down the use of race-based affirmative action in admissions, gives them little discretion in shaping the student body, and have pressed for it to be modified. No other state university in Texas enrolls a large enough share of high-ranking students to be affected by the proposed cap.

Despite a subsequent U.S. Supreme Court ruling that institutions could use race-conscious admissions in a limited way, past efforts to amend the 10-percent law have fallen short in the Senate, where an influential senator, Royce B. West, has blocked all changes. This year, however, Senator West succeeded only in adding a 2015 expiration date to the cap, when the law would revert to its current form, unless the Legislature acted to change it.

The measure still faces a vote in the House, which has approved similar bills in the past. —Karin Fischer