smoke alarm or extra siren

Not sure what you're trying to accomplish.  You can install a smoke alarm in the basement as part of your system.  An extra siren in the basement won't provide any fire protection.

Using an external siren t warn the basement resident of a fire upstairs is a good idea.  If it is too loud, options are 1) i think the new SS3 siren has a volume setting.  2) in any case you can use physical means (something inside the case or an enclosure around it) to reduce the volume to the desired level.

@sevensiamesecats you are correct. The aux siren sound volume can be modified.