New proposed rules changes drafted by Democrats in the House of Representatives could significantly alter how major legislation in that chamber moves forward.

They also could help current House Minority Leader Nancy Pelosi, D-Calif., shore up votes to take back the speaker’s gavel as she faces a tougher-than-expected leadership race. Though Pelosi has the inside track to return as the House’s first and only female speaker, a small group of lawmakers hope to block that re-ascent to power.