Maybe his VP could be the pitbull.
Would it be unconstitutional for Biden to pick Obama as his vice president?
Heres the wiki entry on the interaction between the 12th and 22nd amendments to the 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".[23] 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).[8][24]
Some argue that the 22nd Amendment and 12th Amendment bar any two-term president from later serving as vice president as well as from succeeding to the presidency from any point in the presidential line of succession.[25] Others contend that the original intent of the 12th Amendment concerns qualification for service (age, residence, and citizenship), while the 22nd Amendment, concerns qualifications for election, and thus (strictly applying the text) a former two-term president is still eligible to serve as vice president (neither amendment restricts the number of times an individual can be elected to the vice presidency), and then succeed to the presidency to serve out the balance of the term (though prohibited from running for election to an additional term).[26][27]
The practical applicability of this distinction has not been tested, as no former president has ever sought the vice presidency. In 1980, former president Gerald Ford (never elected to the presidency) was mentioned as a possible vice presidential running mate for Republican presidential nominee Ronald Reagan, and there were some negotiations between the two camps, but nothing ever came of the idea.[28] During Hillary Clinton's 2016 presidential campaign, she jokingly said that she had considered naming her husband Bill Clinton (twice-elected to the presidency) as her vice presidential running mate, but had been advised it would be unconstitutional.[29] Most likely, the constitutional question raised will remain unanswered unless the situation actually occurs.[1]