WASHINGTON — The Supreme Court embarks on a new term Monday that would make Yogi Berra proud: It truly is déjà vu all over again.

The justices will rule on affirmative action for the third time in four years. They will rule on public employee union fees for the third time in five years. They will deliver verdicts on class-action lawsuits and death penalty appeals, as they do virtually every year.

Before the term is out next June, they likely will consider the Affordable Care Act’s so-called “contraceptive mandate” for the second time in three years and update what they meant a generation ago in ruling that states could not place an “undue burden” on women seeking abortions.

“It’s kind of a term of sequels,” says John Elwood, an appellate lawyer who argues frequently before the court. “There are many cases or questions presented from past terms … that weren’t decided the first time, and they’re back now to be answered, hopefully, this upcoming term.”

Other issues that could reach the court this term or next include President Obama’s effort to shield millions of illegal immigrants from deportation, challenges to voter-identification laws and other restrictions, and efforts by merchants such as bakers and florists to turn down same-sex weddings.

So far, the cases granted for oral argument this fall point the court led by Chief Justice John Roberts back in a conservative direction after a year heralded by liberals — for the landmark gay marriage and Obamacare rulings as well as others on housing and employment discrimination, judicial fundraising, and the way legislative and congressional districts are drawn.

The three most important cases already on the docket represent challenges to lower court decisions that the court’s more conservative justices appear eager to hear:

Fisher v. University of Texas at Austin challenges the school’s system of racial preferences for incoming classes. The justices ruled 7-1 in 2013 that the state’s flagship university must show that taking race into consideration is both essential and narrowly applied. Since then, a federal appeals court upheld the practice for a second time.

The school accepts the top 7% to 8% of students from every high school that ranks them, which accounts for about 75% of each incoming class. Because much of the state is racially segregated, that produces a class that is about 4% black and 15% Hispanic.

The school then fills out the class based on students’ other qualities, including race. For instance, it may accept higher-income black students who did not rank high enough at academically competitive high schools, rather than only those who graduate at the top in less competitive schools. That form of “diversity within diversity,” as it is called, may be hard to define.

The case was brought by Abigail Fisher, a white woman denied admission in 2008, who later graduated from Louisiana State University. The lawsuit apparently is not moot because of the $100 she paid in application and housing fees.

A divided Supreme Court upheld the use of racial preferences in 2003, but former Justice Sandra Day O’Connor opined that such preferences no longer would be needed in 25 years. As a result, “this is sort of the mid-term exam for affirmative action,” says Justin Driver, a University of Chicago Law School professor.

It’s important not just for public universities but private ones that receive public funding. And if the court rules against Texas, it could help challengers who have mounted an even broader assault on affirmative action against Harvard University and the University of North Carolina — cases that could reach the high court in the future.

DEATH KNELL FOR LABOR?

Friedrichs v. California Teachers Association threatens the way public employee unions raise money from the workers they represent. In 2012 and again in 2014, the Supreme Court ruled that unions could not force non-members to contribute, but the decisions did not have nationwide impact.

The new challenge, all but invited by the court’s conservatives, comes from California teachers who object to paying for the costs of collective bargaining. They already can decline to pay for the union’s political activities, such as lobbying and campaign donations, but federal law says unions can collect from anyone they represent through collective bargaining.

Rebecca Friedrichs and her co-plaintiffs argue that everything public employee unions do is political, since they work for governments that collect and spend taxpayers’ money. The cost of union contracts, for instance, are borne by taxpayers and affect state finances.

Labor union officials say the ability to opt out of paying for purely political activities is sufficient. As a fallback, the court could change that rule so that workers would not pay for politics unless they opt in — a ruling that would cost unions money but would not signal a potential death knell. About 35% of public-sector workers belong to a union.

Evenwel v. Abbott presents the court with a question it has never answered — what does the constitutional principle of “one person, one vote” actually mean? The answer will be important to Democrats and Republicans, white voters and minorities, in Texas where the case began and beyond.

The Constitution requires states to use total population figures to create congressional districts. But states have discretion when it comes to their own legislative districts. Texas, like all others, uses total population. The challengers in this case say that diminishes the value of their votes in districts with more eligible voters — and gives voters in districts with large numbers of non-voters, such as immigrants, extra clout.

Their effort to demand that Texas exclude non-voters from the calculus would mean that districts with larger numbers of illegal and non-voting legal immigrants, prisoners, ex-felons and children under 18 would take on additional population. That would diminish the value of each vote in those districts, much as the challengers say the value of their votes is diminished now.

If Sue Evenwel and Edward Pfenninger win, it likely would benefit rural and white voters and harm urban dwellers and minorities, particularly immigrants. “It makes a huge difference in Texas and many other states today,” says Gail Heriot, a professor at the University of San Diego School of Law. “Lots of non-citizen immigrants live in urban neighborhoods.”

ABORTION, CONTRACEPTION NEXT?

While the affirmative action, union representation and political district cases are likely to be heard in December, the 2016 portion of the high court’s term is still being fleshed out. It could be highlighted by two cases yet to be granted involving abortion and contraception.

The justices are likely to grant an abortion case from Texas challenging the state’s latest restrictions on abortion clinics. Those restrictions — requiring doctors to have hospital admitting privileges nearby and imposing new physical plant requirements on clinics — would leave only 10 clinics in the state and force some residents to drive up to 150 miles for services.

The state law was upheld by a federal appeals court, while courts in other parts of the country have struck down similar laws. That makes it all but certain the high court will hear the case — and possibly another from Mississippi — in an effort to define what it meant in the 1992 case Planned Parenthood v. Casey when it said restrictions must not impose an “undue burden” on women.

“Abortion is looming on the horizon as something that could come to define this term,” says Leslie Kendrick, a professor at the University of Virginia School of Law. Jennifer Dalven of the American Civil Liberties Union calls it “the most important abortion case since Casey.”

The court also is likely to accept one of many pending cases filed by religious non-profit institutions, such as charities, hospitals and universities, who object to offering health insurance coverage for contraception.

The court ruled in 2014 that closely held for-profit corporations with similar objections can opt out of the coverage requirement by transferring it to their insurers. But the non-profits don’t even want to take that step; Erin Murphy, a lawyer representing challengers in two cases, says they equate the process with “facilitating sin.”

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