I'm not sure just what your definition of "most of the NEC" really means. However, since NY State and the MTA already own most of the NEC within NY State, there really isn't much more to buy and I'm not sure why they would want to buy it and now be stuck with the costs of maintaining it. The only sections of the NEC that the MTA doesn't already own are from Penn Station through the East River tunnels, past Sunnyside, over the Hell Gate Bridge, and up to Shell interlocking in New Rochelle. From Shell east to the CT border, the MTA already owns the tracks.
Additionally the LIRR made a deal with Amtrak years ago that guarantes them X number of slots everyday. Amtrak can not take away those slots, the LIRR owns them. So for the amount of trains that MN might eventually send down the Hell Gate line, I can't really imagine why NY and the MTA would want the expense of maintaining them. And they certainly wouldn't want Sunnyside yard, and I don't see Amtrak selling that. The LIRR just built a brand new facility next to Sunnyside yard, so they have no need of the greater Sunnyside facilities owned by Amtrak.
As for the west side, Metro North already owns from Spuyten Duyvil north to Pougkeepsie. The only section that they could buy is NYP north to Spuyten. CSX owns north of Poughkeepsie. And there were merger plans a few years ago for MN/LIRR, but that got squashed and I haven't heard anything new.
Alan,
Take care and take trains!