Prefix this with: not that this matters at all. There have been a number of recent instances of democrats moving to the Republican Party. From a procedural POV is there anything stopping a democrat from switching to the Green Party, PSL, or the like?
Procedurally, no.
But I’m sure the House Commissioner for Lightbulb & Toilet Paper Maintenance will raise the alarm bells and prevent such a thing in the names of Democracy™ and Civility©