Twenty-second Amendment to the United States Constitution
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. 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).
Fourth Republic of Korea
The 1963 Constitution limited a president to two four-year terms. However, Park won the right to run for a third term in 1969 when the National Assembly, dominated by his allies in the Democratic Republican Party, amended the 1963 constitution to allow the incumbent president — Park himself — to run for three terms. He won a narrow victory over opposition candidate Kim Dae-jung.