My advice to you would be to fill out the forms and seek the aid they are willing to provide. There’s not like melt to be a significant advantage undercutting your request.
For an international seeking aid, my advice 1) know the schools providing intl aid. Good rule of thumb is to Google universities endowment per student. The higher the ratio, the more likely they are to give aid. But verify this against a schools common data set. You can find average award per international there. It will vary year to year, so dont read too much into it if school A is 60,000 and school B is 52,000. That’s likely statistical noise from the small group they admit. But if a schoo ll notes they don’t award aid or if the average is 30,000, that’s a warning.
2) The next step is to understand the relative selectivity of different schools who are generous with aid. All schools in first 4 tiers give good intl aid. The 5th is mixed.
HYPSM
Columbia, Penn, CalTech, UChicago, Brown (maybe a tier below)
Duke, NU, Dartmouth, JHU, Cornell
WashU, Vandy, Rice
ND, Georgetown, NYU, CMU (no aid), Tufts, Emory, USC, etc.
And so on. Liberal arts colleges are also an option. The most selective 5 or so are roughly tier 3. This is overall selectivity. Selectivity will also vary by program strength. Georgetown will be more selective for government/international affairs, JHU for biomed, just about any school for CS, etc.
3) Research the schools. Cut schools you have zero interest in attending or which won’t offer aid. Then prioritize your list. It’s tricky because there is very little difference in applicants between these schools. The majority attending that 4th tier above are top 1% students. But maybe HYPSM are 1 in 200 or 1 in 400 type students. It’s really difficult to know how your application will read, so don’t just apply to the x most difficult schools from tier 1 and 2.
Some people will apply to 25 schools. Some are very discerning. 1 HYPSM, 3 from the next group, 3 from the next, all 3 of WashU/Vandy/Rice, 5 from the group following.
Disclosure: I went to WashU, so maybe I’m a bit of a homer. But I think there is good value in the Vandy/Rice/WashU group in terms of better admission odds while still getting an excellent school with aid. Same with Emory in the next group. Applications are time consuming. If someone is truly competitive somewhere in that range, in hindsight, it’s easy to “waste” energy applying to 7 of the 10 most selective, not get in and never know if schools a bit further down the pyramid would have been successes. Find schools to like across the spectrum and apply to multiple groups.