If I were you, I’d apply EA to both MIT and Case. If you get into MIT, you can still apply to Harvard RD or any other school you please. If you also get into Case, you can wait things out with both MIT , Case, and any other schools, as to what financial aid and merit you might get, as much of that often comes out in the spring.
If you get into Case but deferred from MIT, same scenario. You have Case as an admissions school now , and can apply as above to whatever other schools to see what shakes out. That includes Reach schools like Harvard as well as schools that might have money in the offering.
If you are deferred by Case and MIT, that puts you into a whole other scenario. You have zero schools (unless you have acceptances from some others on an EA or rolling basis) , and you need to do some serious thinking about how much you want to go to Case. Though chances for a RD accept are about the same as EA , for MIT, that you are deferred by Case puts a lot of uncertainty into the situation that wasn’t there initially. Are you prepared to lose out on Case entirely, due to hopes of a Harvard or MIT or like school accept when you did not get a EA accept from Case? You might at that time. (If allowed—Check the rules) change your Case app to ED2. If acceptedED2, that ends your college application process IF case gives you an acceptable financial aid package Be aware that it is highly unlikely you get merit money ED from Case, and by accepting ED, you will have to withdraw your other applications and cannot compare scholarship or financial aid from other colleges at the end of the season.