While answering this Q, stumbled upon this other one: add ‘file upload’ field to user details, which may be a duplicate and where Bainternet suggests Cimy User Extra Fields.
Advanced Custom Fields can do the job.
Without any premium Add-on* this can be solved adding Image fields to the Users pages:
^^^^
Which results in this:
* http://www.advancedcustomfields.com/add-ons/
The Repeatable Fields would make this less cumbersome. And just learned that there’s a new add-on: Gallery, that seems quite interesting for managing images.
But, in those cases, I guess you’ll have to create some jQuery to control the maximum allowed pictures.
You’ll probably need/would-like to restrict the access to other users uploaded files.
See: How to hide media uploads by other users in the Media menu?.