Question: The private school I currently attend only allows for each student to take no more than two AP classes each year. However, I wish to take more AP courses while I am in high school. Would it be wise to participate in a postgraduate program at another school to increase my chances in getting into a selective college?
If your school has a good track record of getting its graduates into the kinds of colleges you're targeting, then it's probably not necessary for you to augment your school curriculum with outside APs. It is a bit unusual for a school to limit the number of APs, but the intent may be to keep the workload at manageable levels. I don't know what the rationale may be.
I know of some students who have been accepted early to Princeton engineering with only four APs on their transcripts, although they did have a number of other outstanding aspects going for them. Thus, the sheer number of APs is not the primary issue. It's your overall profile that counts. If, however, you have a real love of learning and would enjoy taking additional APs outside of your school--and can handle the load--then I can't see anything wrong with that. Be sure to inform your college counselor if you decide to do that.