A complicated story so I’ll try to keep it short. Basically, I was fairly young applying to PhD programs (in psychology) and got into a program where I thought I’d be a great fit. My advisor’s research interests seemed to match up with mine, but the more I started working in the lab I realized how much they....don’t. I’m realizing that we have really conflicting theoretical orientations, and I’m not in any way shape or form thrilled about the current research being conducted in the lab. I’ve been skirting by on the outer rim of their research interests, but I ultimately know for the sake of my future I should be working with someone who has more expertise in what I specifically want to work in. All that said, I can tell my advisor wants me to pursue my own interests and is trying to support my ideas (but it’s clear they are working outside their expertise). I actually have a great relationship with my current advisor and interpersonally get along fantastically with my lab. I feel lost as to what to do (switch labs and work with someone more related to what I want to do-not sure if that would damage any current relationships with my present lab, continue with someone who is very supportive but not in the area I want to be in, something else....). I would feel more comfortable working outside said advisors expertise; however, they are new faculty and I’m not confident they can support me very well in that domain. Honestly just looking for advice/thoughts.... I’ve subtly brought this up in our individual meetings but haven’t done anything drastic.
One statement in your question stands out: "I can tell my advisor wants me to pursue my own interests and is trying to support my ideas". That alone would suggest that, under certain conditions, it might be wise to stay. You have other supporting statements as well.
Some students can carry on their research with only minimal advice from advisors. Others need more continuing support, and even the ideas about what to study. You seem to be more in the former group than the latter, but you need to judge that.
If your advisor were hostile, or even indifferent, to your research goals, it would be better to leave, but in this case, perhaps staying is the best option.
But an advisor can be helpful to you in many ways other than just basic support. S/he can help with process and with keeping you within ethical norms of the field. They can probably also make a fair judgement about when you are done and ready to write up your findings. The general support also implies that they will sign off on the work and write good letters. That alone is enough, provided that you are self driven enough, and with enough ideas, to carry through the research relatively unguided.
You need to judge this, of course, but I would be hesitant to make a quick decision to go elsewhere, either at the same university or at a different one. Imagine what your situation would be if it were completely reversed: a hostile advisor who was very knowledgeable in your specialization.
Think before you jump.
However, there is also an opportunity to get the specific guidance you may want outside your institution. It is harder, but not impossible, to keep close contact. In the long term, you do want external collaborative relationships to support your future career and it isn't unreasonable to begin to develop them now. Your current advisor may even be able to put you in contact with a few people. Conferences are also good for making contacts in some fields.
Anyone where you are with the right interests that you could add to the team? It's not clear how far along you are, but switching is always disruptive. Furthermore, you already have good support and engagement and that should not be undervalued. A supervisor does not only provide technical guidance, but also assistance with helping you think through your research question, structuring your thesis, contacts, planning and managing a research program, and many other aspects of being a researcher.
To me it sounds like you need to have a clear talk with your advisor about your desired approach and ask for assistance about how to achieve that.
Also, can you do some research contrasting your approach and your advisor's - what does each bring to the table? Can they be combined or parts dealt with one way and other parts the other way? People with different views can make fabulous collaborators.
I am in the exact same situation. I unfortunately had to stay with my advisor and am seeking help from other people but it is not easy. If you can, I would recommend switching to someone else. Your future success matters the most.