Twenty-second Amendment to the United States Constitution
As worded, the primary focus of the 22nd Amendment is on limiting individuals twice elected to the presidency from being elected again. Due to this, several issues could be raised regarding the amendment's meaning and application, especially in relation to the 12th Amendment, ratified in 1804, which states, "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States". While it is clear that under the 12th Amendment the original constitutional qualifications of age, citizenship, and residency apply to both the president and vice president, it is unclear whether someone who is ineligible to be elected president could be elected vice president. Because of this apparent ambiguity, there may be a loophole in the 22nd Amendment whereby a two-term former-president could be elected vice president and then succeed to the presidency as a result of the incumbent's death, resignation, or removal from office (or even succeed to the presidency from some other stated office in the presidential line of succession).
2020 United States Senate elections
One-term incumbent Democrat Cory Booker was re-elected in 2014; Booker first took office after winning a 2013 special election. Booker, who is running for President in 2020, could run for both President and re-election to the Senate as New Jersey election laws allow candidates to simultaneously run for two offices. Should Booker choose to forgo a Senate run in 2020, though, potential Democratic nominees include incumbent governor Phil Murphy and incumbent Congressmen Donald Norcross and Josh Gottheimer.