I agree that this could be a problem for the Constitution. I can see a more decentralized system emerging, perhaps the Articles of Confederation being reformed per the New Jersey Plan, given that much of the added territories would be considered small states population-wise and would probably not want to be dominated by the larger states in a centralized system like the Virginia Plan that was revised into the Constitution.
EDIT: Perhaps we could end up with a parliamentary system that way, given that the NJ Plan and the AoC had the executive weaker and elected by Congress.
This seems to make sense to me. From what I've read, the NJ plan still creates a centralized government, just under congress not the executive branch, so it solves the problems of congress not exercising any real power and the states acting independently without tipping the balance I favour of large states or giving a lot of power to one office. The thing is, some historians see the NJ plan as an extreme counterproposal for the purpose of negotiation, so while I see the one state one rep aspect as being very likely to be adopted, I think that greater economic centralization may still be accepted TTL. Federal taxation is super limited in this plan, while the states can impose internal tariffs, which can be a problem. It also lets people just make states in the territories if they have a large enough pop instead to the gradual integration. This isn't something I see as very likely. I feel like congress would still control the integration of new states.