That proposition would change the relationship and impeachment jurisdiction between the Senate and the House that are currently mandated only by the Constitution.
How?
The United States Constitution, Article I, Section 2, Clause 5 provides:
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The House of Representatives ... shall have the sole Power of Impeachment.
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House Practice: A Guide to the Rules, Precedents and Procedures of the House, Chapter 27. Impeachment, From the U.S. Government Publishing Office:
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https://www.govinfo.gov/content/pkg/GPO-HPRACTICE-112/html/GPO-HPRACTICE-112-28.htm
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Sec. 5. Effect of Adjournment”: .....an impeachment proceeding does not expire with adjournment. An impeachment proceeding begun in the House in one Congress may be resumed in the next Congress.
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Sec. 8. Following the adoption of a resolution to impeach, the House appoints managers to conduct the impeachment trial in the Senate.
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So, the “sole power” requires that the rules adopted by the House can only be changed by the House. Yes, the House could change its own rules and the Speaker could appoint themselves.
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Modifying that “sole power” to force changes on the House would require a constitutional amendment.
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That’s how.......