Daniel Collins could soon be a judge on the San Francisco-based appeals court where he’s been a familiar face, despite Democratic concerns that he took litigation positions that they say sought to overturn precedent.

Collins is a Munger, Tolles & Olson partner who’s been nominated to the U.S. Court of Appeals for the Ninth Circuit, where he’s argued 38 cases.

The Senate advanced his nomination on Monday night in a procedural vote to limit debate, 51 to 43, setting up likely confirmation before the week’s out.

He’s opposed by both California Democrat Sens. Dianne Feinstein and Kamala Harris. But Republicans...