Is it possible to develop functions that you 'don't have'? (e.g. NeTi developing Ni and Se)
No... not that I can tell. I suspect type works a bit like gender, where the human-equation has both male and female, but one person is either one or the other. I think we are given one pair of processes to perceive and one to judge. But each pair has all the elements needed. So if you wanted to be more rational, you have a dispassionate process [either Ti or Te] and you'd develop whichever one you have. If you wanted to develop more realistic and concrete perception of reality (like Se) but you're an Ne user, then it comes down to developing Si more since that's the concrete process you'd have.
Considering that tentative evidence shows that certain methods of brain usage are linked to certain cognitive functions (I expect more evidence will be had in the future), it wouldn't really make sense for someone to develop a function they don't even have. To actually 'truly' use that function, someone would essentially have to rewire their brain.
I find it very interesting to consider developing underused functions. And also the oppression of naturally strong functions.
I've been visually typed as NiFe (still consider my video the product of self-conscious expression and thus a flawed sample), but based on reading others descriptions of their mental processes and how they self-manifest, I've understood myself as a NeTiFeSi user with well-developed Fe.
Why would I have a well-developed Fe? Two of the core figures in my early life have been Fe users-my mother (SiFe) and my best friend (FeSi). While we generally get along, I've had so many little conflicts with my mother and my best friend about expressing myself in a socially-acceptable way that I feel like from a young age I developed a heavy self-consciousness about my interpersonal communication that at times came to stifle my natural behavior.
While I'm generally friendly and receptive to the moods of groups I'm in, I run out of my "people points" very quickly, and I've learned to self-censor. This all makes me rather awkward sometimes, because I'm not always sure what is the best way to express myself.
I feel like many of my core decisions in life have been the result of oscillations between Ne-Si and Ti-Fe. I was a grad student for two years. During that time, I felt like I was primarily using Ne/Ti. My style of paper-writing would revolve around shooting out in 30 different directions to gather lots of different info, then condensing it down into a workable single, original argument. While I was good at this and I enjoyed it, I also felt the need to share the ideas I came up with with others. I started to hate how self-contained grad student life was, and how difficult it was to strike up intellectual exchange.
So I did a 360, left grad school and went to work at a community center to get an infusion of everyday practical reality. Here much of my life is interpersonal skills (Fe) and administrative info processing (Si). I'm pretty good at my job, but I find the admin work incredibly boring. I also dislike how little I'm able to use my ability to come up with many possibilities and then condense them into workable ideas. Here I don't get to discuss ideas very often. To much sharing, not enough ideas-in-the-sky creation. I have gotten better at procedural activities (Si) and interacting with others (Fe), but I wouldn't say that I'm the greatest or that I enjoy either of these things immensely.
So now I'm going back to grad school . But I want to do my best to avoid feeling trapped in self-containment like I did last time. I'm good at lonely analysis, but I find it too lonely. I like being around people, but mostly only if I'm discussing ideas. So I'm seeking a balanced cycling so that I don't have to drastically change lifestyles every year or two.
It is interesting to observe how you can develop functions and get better at manifesting them when necessary, but not always feel totally comfortable in that skin. It's hard to stay in it for too long.