Nancy Pelosi is returning as speaker of the House of Representatives amid a partisan standoff that has made it virtually impossible to move forward on major legislation requiring the support of both Democrats and Republicans.

Now, she has a chance to fix at least part of the problem.

Prodded by some House Democrats, in late November she agreed to establish a more open process for working on legislation and to allow more votes on amendments supported by both parties. The changes in rules, expected to come to a vote after the House reconvenes Thursday, will help set the parameters for Ms. Pelosi’s second stint as speaker.

Historically, amendment votes have been critical to legislation, allowing in a variety of ideas. They are one way for lawmakers to change a bill’s contents after it goes through committee, or when it skips that step entirely. They are often used on spending bills to get lawmakers on record on important issues and to build consensus solutions.

But since the House began using electronic voting in 1973, minority party members have increasingly adopted the floor amendment — one of the few legislative tools available to them — as a way to force their opponents to cast politically difficult or symbolic votes. In response, House majority party leaders have clamped down on amendments to shield their members from those electorally risky votes.