In 1787, it's constitutionally possible--but only in terms of the letter of law, though not its spirit. Consider the case of Maine, Kentucky, and Tennessee: they existed as subdivisions (a county in the case of Kentucky) of Massachusetts, Virginia, and North Carolina for some time before they became states. There's not a lot that the parent states could have offered their constituent parts to make separate statehood less appealing: as part of Virginia, Kentucky would not have its own Senators, for example. This means less access to federal jobs and federal resources.
Today, a move to federalize a state within the US federal structure would be problematic because of the incorporation of the Bill of Rights against the states (i.e. 14th Amendment and associated jurisprudence). For example, Georgia used to elect its governor under a semi-electoral college system in which the victor had to win a majority of counties, rather than a majority of votes. In late 20th century, the US Supreme Court ruled this violated equal protection by failing to provide for one-man, one-vote. This doesn't make a sub-federation impossible, simply unlikely.