Mandarin Chinese allows implicit, non-canonical, and quantity-objects. The first type is seen in Wǒ zhǎo-guò-le ‘Lit.: I looked for’, which means ‘I have looked for some entity that is known to the interlocutors’. The second type is seen in Lìlì qiē-le nà bǎ dà dāo ‘Lit.: Lili cut that big knife’, which means that Lili cut something with that big knife. The third type is seen in zǒu-le yī lǐ ‘walked one mile’. From the perspective of the interaction of yòu ‘again’ with different kinds of objects, this paper shows that while implicit objects and quantity-objects behave like explicit canonical objects, non-canonical objects do not behave like canonical ones. This paper provides new evidence to support Zhang Niina Ning’s (2018, Natural Language and Linguistic Theory 36: 1395–1437) claim that a non-canonical object restricts the meaning of the verb, rather than saturates any argument of the verb. It also supports the internal argument analysis of post-verbal quantity expressions.