it's open enrollment so you can go in and take any course you want. i'm not too familiar with the program but i wonder...can you just take those courses, do well, and get them to sponsor you? what's the difference? or...would your school where you got your BA sponsor you even if you take 28 credits at hes? you should call them up and ask. btw, boston is a great city...not that you'd care with all those classes 😛
You don't need the diploma in order to gain sponsorship - to be honest, I'm not really sure what the benefit of the diploma is. I'm also ineligible for it since I had a semester of chem and a semester of bio in college. There are two separate things - the pre-medical diploma, and the Health Career Program (HCP). You can do both of them, but you could also just do one or other other (although I'm not sure why you'd do the diploma without doing HCP) and I think that actually, most people who do HCP do it without pursuing the diploma. Look at the website and read about HCP and sponsorship:
http://www.extension.harvard.edu/hcp/default.jsp
Basically, you apply, pay your $100 fee, and you are part of the "Health Career Program." (There is a fairly active student society... sign-up sheets are passed around each semester... so you can get to know your fellow students and participate in social functions, etc..) Then, you take a certain minimum number of classes from a list of "medical sciences" classes - this number is dependent upon your undergrad GPA, and of course, practically-speaking, you need to take as many as you need to meet med school admissions requirement. (See the sponsorship link - a number of classes, including upper-level electives, count. Your options for classes are not just limited to those that you must complete if you want the diploma.)
Then, you check in with HCP once a semester. If you complete the required number of courses satisfactorily (B or above, I think) you may apply for sponsorship. This is $500, but from what I hear, it's well worth it and the Harvard sponsorship is valuable.
Just a note - I did not know this was the case, but I have been informed that you are eligible for Stafford loans if you are a half-time student in the Health Careers Program (even if you're not pursuing the diploma) even though it's not a degree-granting program. This would not be the case if you were just taking classes but not formally affiliated with the Health Careers Program.
Oh, and I suppose if you were a recent college grad, maybe your undergrad institution would sponsor you. But why would you want to do that? The Harvard recommendation carries some weight, and since the sponsorship includes a summary recommendation with excerpts from your profs there, it seems like this would be the most relevant sponsorship.