Let me offer some different advice (as a Harvard alum). Volunteering is not actually looked upon as a category in the way you might think:
What the Top Ten schools are actually looking for is not if you have volunteering experience - they are looking for some indication that your professional career is not all about you. That you can be "other focused." That your job is not just all about yourself.
And, yes, a lot of times that criteria is met by volunteering (though in my opinion, tutoring and teaching never impressed me as something unique, as so many people put that on their applications...however, STARTING a tutoring non-profit in India, for example, did impress me a great deal).
What the admissions committee is really trying to "hunt out" and unearth though, is if maybe you're just a finance professional (for example) who spends 80+ hours a week in the office and is only interested in making money and getting promoted as fast as possible, with no thought or care towards anyone else. The schools want to make sure that that self-centered, self-serving, narcissistic person is NOT YOU, and that they don't admit someone like that into their class.
There are ways to demonstrate that that's NOT YOU though without specifically volunteering, and in ways you may actually already be doing but not even realized.
For example: Do you give to any charities? Have you donated to any humanitarian causes? Have you ever? When you paid your taxes last year did you fill out a line for "charitable deductions?" That counts. Volunteering is not always just about volunteering your time, it can be about volunteering your resources too, and that is an area most people forget.
The strategy is to then make a case for your humanitarian donations in your application as a real and valid thing, and then back that up when necessary in your essays or interview.
One of the best ideas I ever saw that got a client in to MIT Sloan, for example, was just an IDEA to start a non-profit. It wasn't even an organization they ever started to build, it was just an idea on paper. This too can impress the committee and count (of course, I would hope it would be a real thing you were thinking of doing one day, and not just a ploy to get in).
All of these ideas are things that have worked though. I have had MBA clients get into the top schools without having any volunteering experience at all. You just need to show somehow that it is not all about you, and to show something that is hopefully unique, as that will make you stand out in your application.
Hope that helps!
[I'm a former Harvard admissions interviewer and a Harvard grad, and currently run the MBA & EMBA admissions firm MBA IVY LEAGUE: Contact me today for more information! https://www.MBAIvyLeague.com]