Nazir 19 - Deriving different things from the same word
A nazir is forbidden to visit a cemetery. If he accidentally comes in contact with a dead body and thus becomes ritually impure, he needs to purify himself, shave all his hair, bring sacrifices, and restart being a nazir. Say he became impure again, on the night before he could bring the sacrifices. Then later he will need to bring two sets of sacrifices. Why? - The Torah said, "He shall sanctify his head on that day and restart being a nazir" - even if he did not bring his sacrifices yet. Thus the new impurity happens to a fresh new nazir, and causes another obligation.
This is the opinion of Rabbi Eliezer. It results in bringing the most sacrifices. The Sages also pay attention to the extra words of "on that day," but it teaches them that that he does not restart his being a nazir until he brings the guilt offering. Thus, right now he has not started another term yet, and just needs to purify himself. This is all one long period of impurity, and later he brings only one set of sacrifices.
This seems to cover all possibilities. But Rabbi Ishmael says something else: if he did not bring all sacrifices, including the burnt offering, he is still not a nazir again. Until then, he only brings one set of sacrifices when he finishes being a nazir.
Practical law? - Follow what the Sages have said, since they are the majority.
Art: View of Pere Lachaise Cemetery by Pierre Courvoisier