Q. Can an announcement be sent with more than one attachment?

No. 

For two reasons it is better to link documents in the body of the Announcement.

(1) You can link to as many documents as you want in the body of the Announcement and (2) students will immediately have access to the documents if you link to them in the body of the announcement (they do not see attachments in the emailed Announcement).  To link them in the body of the announcement, put your cursor in the body of the Announcement where you would like it to appear.  Next, click "Files Tab" in the right sidebar.  When you click on the "Files tab", you can either find the file you want by clicking on the “Course Files” link, or you can upload a new File from your computer by clicking on the “Upload a new file” link.  Once you have selected the file(s) you want, the link(s) will now appear in the body of the Announcement.