Ulysses S. Grant made a serious attempt at a third term in 1880. However, he was urged not to run for a third term in 1876, and even said he was grateful to be done. Why the change in heart? Could he have been a three-term president? If so, how?
If you mean, could he have won in 1876, No. The Republicans were at a severe disadvantage after the Panic of 1873 and the revelations of the scandals in the administration. The only Republican who would have any chance of winning in 1876 would be someone like Hayes who could plausibly claim to be a reformer and could win the support of many 1872 Liberal Republicans.
1880 was a different story. One minor point is that in 1880 Grant could more plausibly claim that the anti-third-term tradition should not apply, because it only really applied to a third *consecutive* term (the point being concern about a president using the powers of his office to perpetuate himself there). More important is that like many ex-presidents Grant had grown more popular after leaving office. In fact, Grant was actually the front-runner for the GOP nomination in 1880. He was at the height of his popularity when he returned from his triumphant world tour. His problem was he came back from the tour a little bit too early, giving people time enough to think of his disadvantages as a candidate. Still, for all the memories of corruption in his administration, he was a popular hero, the Democratic candidate (Hancock) was somewhat inept, and so if nominated Grant might have won--though like almost all Gilded Age presidential elections it would probably have ben very close.