Dear Tom,

Anyone who is looking at jobs in the private sector does "multiple" job applications concurrently.  The agencies involved normally do not care unless you have not completed someone else's process due to background issues.

From an employer point of view, you might be questioned on which one of your applications you would prefer and have to defend your opinion.

If you get further into the process, the FBI background forms will ask you for all of the agencies you applied for and the disposition of those applications and any interviews and tests you took during the process.  Failure to completely disclose all information will be grounds for dismissal of your application (and further blacklisting from federal employment).

Regards