Under some circumstances Roman names included an additional cognomen, called an agnomen. These were the exception to the general rule that cognomina were not complimentary.
- Adoptive Agnomina
- In the case of adoption, the original nomen of an adoptive child was used in adjectival form as an additional cognomen. As an example, when P. Aemilius L. f. Paulus was adopted by P. Cornelius Scipio Africanus he used the name P. Cornelius P. f. Scipio Aemilianus. "Aemilianus" is the adjective form of "Aemilius".
- Honorific Agnomina
- Sometimes very eminent Romans were given honorific cognomina in recognition of their great achievements. These were the exception to the general rule that cognomina were not complimentary. An agnomen may refer to a victory over a particular enemy people (e.g. Britannicus, "victor over the Britons") or in a particular place (e.g. Africanus, "victor in Africa"). An agnomen might also refer to a particular virtue (e.g. Pius, "dutiful"; Sapiens, "prudent"), or to general preeminence (e.g. Magnus, "great"; Maximus, "very great").
- Matronymic Agnomina
- In very rare cases a Roman might use an extra cognomen formed from his mother's nomen. The -ia ending was replaced with an -ianus ending or an -inus ending. For example, M. Porcius Cato had one son by his first wife Licinia, and another son by his second wife Salonia. Each son was called M. Porcius Cato. To tell them apart, people called them M. Porcius Cato Licinianus and M. Porcius Cato Salonianus.