You can only have one action statement for a form... but that action can point to a script that can do any number of things.
Here's a rough outline (treat as pseudo code... it's probably riddled with errors)
//Do other stuff
//e.g., Store in a database
//e.g., send an email
<form action="<?php echo $_SERVER['PHP_SELF'] ?>" method="post">
<input type="submit" name="submit" value="Save">