How can I work on standing out on Ivy League applications?

Your grades and extracurriculars are great! However, something a lot of colleges look for is a "spike," or a specific subject or area that you have shown significant interest in. For example, a student with a computer science spike might have taken many programming classes, designed an app, or created a website. Similarly, I would suggest finding an area of interest and pursuing that to your fullest ability. You seem to have an interest in public service and medicine, so maybe you could start a non-profit or take online courses about anatomy, biology, etc. Also, you don't need to be a leader in a bunch of clubs or activities; showing that you put a lot of time into one or two extracurriculars and obtained a leadership position there is more than enough. As of now, you are a very well-rounded student; just work to develop a spike and you will be an extremely competitive applicant.

As for what Ivy Leagues look for... well, I'm not sure anyone knows for sure. They do want to see that you've challenged yourself and pursued your interests. Just do what you enjoy, keep studying, and you'll do very well.

Hope this helped!

The best way to stand out for an Ivy League school is to, well, not focus on "getting into an Ivy League school." It's not really a mystery; Ivies, and most top universities, look for students who are intrinsically motivated and passionate about something. Whatever that something is does not particularly matter—it could be woodworking, writing, designing video games, flying planes, really any kind of interest or hobby or passion that sets that person apart from other people who are similarly academically strong.

Try to figure out what you care about—like @akashi23 said, it sounds like that could definitely be medicine, public service, or some combination of the two—and continue pursuing it. Volunteer, continue your involvement in your clubs, but also learn about it on your own time. Find people you can learn from and volunteer with. Then, when it comes time to apply to these places, you'll have something you really care about and have developed your interests in that you can write your essays about. That's how you stand out; show that you care about something.