I've installed the Invite module. I see that there is an extra block that you can active. When you do this you will see a block like this on your page:

But I would like to have this field on my user/edit page. And make sure that they can enter multiple e-mail addresses separated by , .
But how can I do this?
mail()already accepts comma-separated addresses, and as far as I know Drupal by default uses it. So maybe no alteration is possible, and simply setting block to display on user/*/edit would be enough?drupal_mail. We need to know what the OP has tried though for obvious reasons