Only for reelection and President (or VPOTUS)
If it makes sense for the federal executive, why not also permit running for governor and state legislative office at the same time and give up the lower office if successful at both. Or why not mayor and city councilman?
With the exception of elected judges, most states treat running for reelection as equivalent to running for an office the first time (unless they are term limited). Incumbents already have significant advantages, and I wouldn't suggest giving them additional advantages.
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