Hello @sn0399 and welcome to the Canvas Community. Is this an assignment where you needed to record media using Canvas or upload an audio or video file? I just tested in a sandbox course with test students and as a student I was able to record multiple files in the media upload option of an assignment as well as upload multiple files. When looking from the student perspective, on the assignment page I see a "re-submit assignment" link. Is this not visible for you?
From the instructor perspective, I see every version of the assignment submitted. There isn't a way for someone to delete a file they have already submitted but submitting multiple files should be possible.
If you don't see the re-submit assignment button, you might try opening Canvas in a couple of different browsers, such as Chrome and FireFox. Sometimes that makes a difference. If you still don't have luck, I would submit a ticket with Canvas Support to see if they have insight into what you are facing.
I hope this helps and best wishes.