General synonyms:
* Other
* Different
* Additional
* Further
* More
* Second
* Alternate
* Extra
* New
More specific synonyms:
* A second (referring to a specific number)
* A different (emphasizing a distinction)
* An alternative (referring to a choice)
* An additional (referring to something added)
* A further (referring to something beyond)
The best synonym will depend on the specific context and the meaning you want to convey.