Accidentally stumbled upon your thread when I was checking out new posts. It's a happy accident :-)
I think this is a very interesting thread, and judging by the varied responses, you have struck a chord with many people.
Can you be yourself without changing?
Um...I'm not sure if I have understood this question properly but I'll try adding my 2c anyway...
I think this largely depends on what is being changed and your reason for the change. As Tony WK said- I'm paraphrasing- if it's a behavioural change that has to do with being considerate of other people (or animals) then I think that you can still "be yourself" in those instances. Apologies to Tony WK if I have misinterpreted your post.
But I think if the change would require uprooting core aspects of yourself (and not only, say, behavioural changes) e.g. values, principles, beliefs, etc then it might be a different story.
Is it possible to change/improve a part of yourself and still be yourself?
Um...fence sitter in me says "yes" and "no." Again, my 2 cents is it depends on why you want to change/improve and how much that change would affect your sense of "self" as you previously knew.
For example, if you wanted to change to (purely) please other people then maybe you're compromising core aspects of your personality in the process. But if you wanted to change because you felt like your actions were hurting others then I feel you can still be true to yourself in those situations.
The other thing is that I think people evolve...most people don't just emotionally or intellectually stagnate at one point in their lives. To an extent, I think change is inevitable...whether you still feel like "you" after a series of changes will vary from individual to individual.
Also, I agree with James' point about how people aren't extremes but we are on a spectrum. Say, just because one identifies as being "introverted" doesn't automatically mean that he/she won't have situations where he or she is the life of the party. Similarly, a person who identifies as "extraverted" can also have moments where he/she just wants to be alone. I like to think we all exist on spectrums of personality and human behaviour. Moreover, we aren't rooted at any one point on any given spectrum...there is room to move in my opinion :-)
Anyway, that's it from me for now. I don't expect everyone to share the same views as me but I just wanted to chime in with my subjective take on it :-)