If I understand you, no you cannot. A database restore will overwrite the destination.
It sounds like you are wanting to merge one database into another, which can be done with 3rd party tools.
You would need to
- Restore the backup to another database
- Merge the newly restored database into the current database.
If this is a task that you need to repeat, then you could probably create an SSIS package to help you automate the process.
If you have a search for SQL Merge tools, or look at this question
A restore is replacing the database, its not running any kinda of insert or update transact sql it really is just overwriting the database.