Allow multiple taxonomy term selection with simplenews to send emails to multiple mailing list ?

Hello,

I created a private newsletter for a client, with several mailing lists. Only the client can add users to the mailing lists.
The problem is that sometimes, he wants to send the same newsletter to 1 or 2 of his mailing lists. Actually he must create twice his newlsetter...

So here's my ask ; Could it be possible :
Neither to have checkboxes instead of selectlist to select several mailing lists ;
or, if it's not possible, to not disable the newsletter after sending the mailing (this way the client can edit again the newsletter and resend it. but I would prefer the first option)

In both cases, I'll need it quickly ; so could you explain me how your code works so that I can try to modify it for my needs ? What is it's logic ?

Whitch function creates the form select to choose the mailing, and whitch one gets this information and go searching the users list ?

Thanks for your help ;)

Seren