In PHP, is there any harm in running session_start() multiple times?

As of PHP 4.3.3, calling session_start() while the session has already been started will result in an E_NOTICE warning. The second call to session_start() will simply be ignored.You could check if the session has been started first or not with:

if (session_id() == "")
  session_start();

From the docs:

As of PHP 4.3.3, calling session_start() after the session was previously started will result in an error of level E_NOTICE. Also, the second session start will simply be ignored.

So no, it won't "cause harm", but it'll throw an error. And the fact that it's happening is probably an indicator that you're doing something incorrectly, and might need to re-think how your code is laid out.