What might an Asymmetrically Federal United States look like?

Background:

How might such a system work within the United States? While the typical example of asymmetric federalism is a system in which a few states have more autonomy, it could also be a system in which a few states have less autonomy. Or both.

The scenario that is easiest to envision is one in which Quebec joins the Thirteen Colonies, and when the Constitution is drafted, argues for more autonomy due to its cultural differences.

Another scenario that is less likely is some compromise surrounding the debate on slavery or Reconstruction.

In either case, I could see some additional autonomy (such as the right to secede, or explicitly giving special privileges such as protecting slavery or the right to establish a state church) in exchange for less representation in the Senate (either just one Senator, or perhaps two with ‘normal’ states getting three).
 
Maybe a situation where the "original" states have a special status, and those subsequently admitted are seen as essentially "artificial" creations, being created basically out of units of administrative convenience, and have sort of a "second-tier" status?
 
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