There is considerable debate about that.

> States are not allowed to make agreements with each other parallel to the system.

Yes, they are. In certain circumstances, such agreements require affirmative Congressional consent, though its questionable if the National Popular Vote "Interstate Compact" would meet the standards for requiring such consent, whether it would require only negative consent, or whether it would be outside of Congress' authority because of the assignment of the power of choosing electors.

> if you can get that many states to agree to it, then you could have just done a constitutional amendment

No, that's not at all necessarily even approximately true. For it to be effective, you need jurisdictions with a bare majority of electoral votes to implement it. For a constitutional amendment, you need 3/4 of states.

The minimum number of states to hit a majority of EVs is 16, as opposed to 38 for a constitutional amendment.

> since all you need for that is for the states to agree, and the senate to agree.

You don't need the Senate to agree to a Constitutional Amendment. You need 3/4 of state legislatures to agree. You can propose a constitutional amendment with 2/3 of both houses of Congress, or call a Constitutional Convention on the application of 2/3 of states.

Both proposal and ratification (presuming senators vote in line with their states, regardless of the House) have a higher minimum threshold than would be otherwise required for states representing a majority of EVs to assign electors in line with the national popular vote and determine Presidential elections that way.

Uh, no. 38 states have to ratify an amendment in order for it to take effect. You can easily eclipse 270 electoral votes without getting the support of 38 states.

Specifically:

>No State shall, without the Consent of Congress, ... , enter into any Agreement or Compact with another State

In this case, since such a deal is changing how the president is elected, and changing the balance of power between states and the fed, it could probably be seen as encroaching on federal power. So simply getting congress to pass a resolution approving it (which in theory would solve the "consent of congress") wouldn't fly like it would with an interstate compact dealing with something more mundane and less political like water rights, or mutual deal on air pollution between several neighboring states.

Disclaimer: IANAL, this is not legal advice etc.

2) the part that says no interstate compacts without express approval of congress