You can add as much as fields as you want. The students would fill them according in their seetings page (here you could change the name for one more appealing) and those fields are searchable by default so you would not have a problem with it.
Bu BuddyPress does all you want out of the box.
Thanks your for your answer. I guess I did not make myself clear enough.
Each user should be able to add as many of these fields as he or she likes. If one had done many jobs in his career one would require a lot of the aforementioned fields. If I’m a young grad student there are probably not gonna be too much. That’s why each user should be able to duplicate the initial field group to have as many as he wants.
I don’t think Buddypress can do this out of the box. I looked at database structure and it seems each user can only have one field assigned to field of a group (1:n relationship).
I’m sorry @jancbeck, I wasn’t understanding what you wanted. Now I do and can’t think of a way, but if I come across of something, make sure I will let you know.
you should also look at an old plugin called BP Resume it nay be of some use to you…. I tweaked it a bit at smeak.com and it works quite well

Awesome @maddogmcewan! Thank you for sharing! =)
@maddogmcewan great tip – thanks! Unfortunately though, it allows neither file uploads nor are these fields searchable. I’m investigating using ACFs repeater field in combination with a front end form but this is also far from being perfect.
@jancbeck Maybe with a few coding that would be possible…
I know this thread is over a month old, but I have a question about this plugin. Has anyone successfully modified it to allow for the editing of entries? It looks like the only options are add and delete. “Edit” would really make this plugin complete, though.
I plan on using it for something a little different than resumes, and my using will probably be editing their entries a lot — so forcing them to delete and rewrite them each time would probably make me public enemy number one.
@cappazushi
Don’t listen to that BS. If that person that replied above that mentioned that plugin really wanted to help then they would period. That user is a phony and I will leave it at that!
@cappazushi
Matter of fact that particular users site moves at a snails pace so in reality whatever they did was garbage because who wants to wait for a site to load when it takes 2-3+ minutes?
The developer’s site may be lame, but he developed a much needed (if incomplete) plugin for BuddyPress. It isn’t slowing down my test site, by the way.
I’d just like to figure out to modify it to work…well, fully. I’ll be using it for listing collections, by the way — not resumes.
If you can’t help, then, thanks for the bumps. Be nice.
@jancbeck – i haven’t done much lately to improve the plugin, for me I think next step would be to add the ability to edit fields, then step 2 would be to incorporate some xprofile fields – if i do anything I am happy to share