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Hello,

I'm sorry but that's not possible.
Profile ID is stored inside your Joomla session, this means that you are "stuck" with the same Profile ID as long as the backup process is running.

this means I have to do the configuration on database/file level in the meantime? Or can I use another browser having another session?

I strongly suggest to avoid directly writing in the database, there's an high chance to break your installation.
You could use a different browser and a different Joomla user to be sure to not invalidate your backup process.
However the best thing is to simply do your configuration work before and then run the backup. Or even better use automatic backups so you don't have to bother about this.

If you are using Akeeba Backup 4.6 or earlier what Davide said is mostly correct. You'd need to log in with the same or a different user from a different browser (or your browser's private browsing mode) to start a new Joomla! session and handle the configuration. There is no need to log in as a different user since Joomla! 1.6.

Since Akeeba Backup 4.7 this is not the case. The only thing you do need to do is keep the page where the backup is running open since, well, it's the browser which acts as the backup controller (step through the backup) to avoid server timeouts.

If you have another window / tab to your site's administrator open you should be able to modify a different backup profile. Please note that if you try modifying the profile being used to take a backup, or remove it, things may go bad.

Also note that if a backup step is taking over 3 minutes to complete, going back to the Control Panel page will cause the backup to be marked as "failed". If the backup is still running at this point it will crash.

We do not recommend interacting with the configuration of Akeeba Backup while the backup is running since things may go bad. However, nothing really stops you from doing it. Just be warned that if it breaks you get to keep both pieces :)