Normalizing multiple audio files

I have a project that involves many voice over files, that all need to be amplified. At the end of the day, they all need to be brought to roughly the same level of roughly -8 db.

I had thought about normalizing each one, but I am under the impression that this will not amplify them equally. If one or two of the files has a relatively loud sound. Normalizing will make the overall file quieter. Am I correct.

What then is the best way to do this? To amplify by the same amount?

I am using adobe audition, and as far as I can tell, if you normalize one file (for a reference), it won't tell you how much you amplified it by, so I can't use that to create a reference for a batch process.

I'm sure I am not making much sense, but I guess my overall question is where can I find a good method to batch process multiple files to have them all end up at the same relative volume?