Emacs obviously can handle multiple asynchronous sub-processes, otherwise a multi-language programming environment like org-babel, to give an example, wouldn't be possible.
However, when I'm in Dired and start an asynchronous shell command to view a pdf file (& evince), and then try to do the same on a second pdf file, I get the following message:
"A command is running - kill it? Yes or No?"
Is there a way to run several asynchronous shell commands in parallel, when in Dired?
I don't think it's possible with dired-do-async-shell-command, but if you just want to open some file is certain external application I suggest using OpenWith, which allows any number of external processes running.