BOSTON (AP) — Anticipating renewed fights over abortion, some governors and state lawmakers already are searching for ways to enhance or dismantle the right in their constitutions and laws.

President Donald Trump's nomination of Judge Brett Kavanaugh to the U.S. Supreme Court has raised the possibility that a conservative court majority could weaken or overturn the 1973 Roe v. Wade ruling, which created a nationwide right to abortion. That could fan an already raging battle in states over what should and should not be legal.

While a complete reversal of Roe remains a longshot, some Democratic...