When I log to my S3 console I am unable to download multiple selected files (the WebUI allows downloads only when one file is selected):
https://console
The S3 service has no meaningful limits on simultaneous downloads (easily several hundred downloads at a time are possible) and there is no policy setting related to this... but the S3 console only allows you to select one file for downloading at a time.
Once the download starts, you can start another and another, as many as your browser will let you attempt simultaneously.