Joedoe, haha, is there any such thing as a "normal" student?
I do know students with higher level physics, more than one chem, greater than Calc 1, have their applications immediately moved to a different pile, according to admissions and scholarship grantors at leading engineering schools. "Moving to another pile" does not grant guarantees of admission, it merely means they want to take a close look at these students and yes, they are desirable.
I was the Regional Scholarship Chairman for FIRST Robotics (about 4K students). As such, I worked closely with admissions and scholarship grantors at many of our best universities. These professionals like to see extensive classes because it indicates preparation on the part of the student and it also speaks to the quality of the high school (more important than you might think). So, it would make sense, since most academies are engineering focused (and so many of the students major in engineering or STEM disciplines), maybe, academy admissions would like to see higher levels or multiple math and science classes on an application. On the other side of the equation, I do know, when admissions reps at these same universities receive an application from a student who has gone all the way through lineal algebra in high school or has taken differential equations, the reaction from admissions is akin to a red warning light. They want a personal interview to make sure the student can, at least, walk, talk and maybe do their own laundry. Sometimes, they are looking for more "normal".
Academies are also very different and so many posters here, with far more experience, consistently indicate there is NO MAGIC FORMULA for admission. Here, leadership qualities, grace under pressure, the ability to communicate, ethics and physical ability would be far more highly valued than at School of Mines, Ga Tech, Carnegie Mellon, UPenn, Renssalaer, Stevens, MIT or a Cal-Tech. Like my son says, the reason he wants to go to USAFA (besides being an officer) is that he knows, it will make him a better "whole" man. Besides, as we all know, most Cal-Tech students would never survive the first month at USAFA.
In conclusion, don't over load senior year. Reach, yes, but do not burn out. If you are one of the chosen few, you will need all your strength. Best wishes.