Here’s a simple way to look at it.
Applying to Stanford does not increase your odds of getting in to Harvard. Getting in to Stanford does not increase your chance of getting in to Harvard. The two decisions are independent of each other. There is, however, a correlation between the two, in the sense that a super-qualified student that Stanford would want is more likely to be someone that Harvard might also want.
However, actually applying to Stanford definitely increases your chances at getting into one school - Stanford. That chance may be very small, but it is zero if you don’t apply. Actually applying to more such schools will not increase your chances at any one school, but it does put you in the running for more schools.
If your chance at Stanford is 2%, and your chance at Harvard is also 2%, this does not mean that your chance at one or the other suddenly becomes 4%. You are the same applicant you always were, and your chances at each school remain the same. But having another committee considering your application is another chance to get admitted to one of these schools. There is no way to quantify the math to know exactly what your overall probability to get into one great school is, and it probably hasn’t changed much with each application - but it has changed a little tiny bit.