WASHINGTON—House Speaker Nancy Pelosi (D., Calif.) is split with her leadership team over how to handle moderate Democrats who are siding with Republicans on procedural votes to carve out independence from their party.

Mrs. Pelosi is telling members to stand together to oppose last-minute changes introduced by Republicans before votes, while House Majority Leader Steny Hoyer (D., Md.) and Whip Jim Clyburn (D., S.C.) have permitted some lawmakers facing tough re-election races to split with the party line, several aides said.

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