In this scenario no one is actually changing. I am still an extrovert. He or she is still an introvert. But we respect each other's needs enough to BEHAVE in ways that take care of each other. And yes, you can "ask" for this. I would argue if you don't ask for it you may not get it. And if your partner is not acting in ways that support your deepest needs then they are not doing their job and you are not getting the benefit of being partnered. And over time, this lack of support for your deepest needs may begin to erode the positive feelings towards your partner. The relationship will no longer feel like a place where you can get important needs met.
Where many of us go wrong is in confusing how we want our partner to ACT and who they ARE. We feel disappointed that our partner is not a certain way and forget that we can ask for behaviors that feel good to us, and that our partner can behave in those ways even if it's not their personal default. Of course we need to learn to ask in ways that are respectful and kind and still honor our partner's own needs and wiring.
For an excellent in-depth explanation of how your partner is wired and what is likely to come naturally to them (or not!) see Dr. Stan Tatkin's audio program Your Brain on Love or his book Wired for Love. Or for those of you who are not yet partnered see Dr. Tatkin's book Wired for Dating. Learning how your partner's brain is set up will help you appreciate why they do what they do (and don't do), how to ask for what you want and need and how to take excellent care of them in return.
Wishing you health and happiness in all of your connections,