When a user wants to attach more then one file he/she should be able to do it with one action - meaning be able to attach more then one file in each attachment action.
Gmail sorted it out last February (http://gmailblog.blogspot.com/2009/02/updates-to-attachments-multi-select-and.html) so you can see the implementation there.
A similar request was submited in 2002 (id 556242) but there was a comment saying "this can't be done with the HTTP file upload
facility" - i think it's time to look into it again.
As was mentioned back in 2002, it cannot be directly done with HTML, and HTTP. GMail is heavily dependent on JavaScript, and AJAX. If you disable JavaScript support in your browser, and then hit gmail, or even click on the "basic HTML" version in the bottom right, you'll get exactly the same behavior you get in SquirrelMail. SquirrelMail tries to be as free from dependencies as possible.
I guess we could look at it as an alternative, but would require a lot of rework of the compose screen to work.
There is a plugin called "Multiple Attachments" that allows adding more than one file at a time (per page request), but the actual file dialog selection is still one at a time -- changing that would be more involved and may or may not be worth the effort.