Can I submit more than 3 reference letters with my grad school applications? Is it acceptable to attach additional reference letters to an application under the supporting documents category of an application? Say I have 3 references from my masters institution, and another 2 from my undergraduate institution. I would think that if they are all positive, that the more is better. Would this be acceptable or is it a no-no? I am particularly thinking about top-10 universities.
No!

US institutions expect that you have never seen your recommendation letters; your references are supposed to upload/submit them directly to your target departments.  But presumably you are uploading/submitting your own supporting documents.

If the application web site somehow restricts you to naming only three references, then you only get three letters; choose wisely.  If it's a paper application, just ask all your references to mail in their letters.

(I assume you are applying to a graduate program.)