There are currently - don't know for sure - in the vicinity of 5,000 identified VAMs. No accurate estimate could exist regarding how many are left to be found, and here's why:
1) They were minted in unprecedented numbers, using unprecedented numbers of die pairs for the coin size. Millions, each year. Dozens of die pairs shipped to each Mint - as many as 90+ pairs for a given year/mint - and those were used in a vast array of combinations. Old dies with new ones, a reverse cracks and is replaced by a brand-new one mated to the same obverse. All of these combinations are potentially VAMs.
2) Die production technology of the time was maturing quickly. The overall resemblance of one die to the next presents the very real question, "Will we
ever be able to accurately tell all these dies apart?"
3) Morgans were destroyed by the millions for the Pittman Act. We'll probably never see examples of a large number of Morgan die pairs, some of which might have had critical transitional information from their working hub as it aged, striking new dies.
4) The initial differentiation process, as Van Allen and Mallis defined it with their work in the 1960's, was to define/list by die characteristic and not necessarily die pair. They were well aware of the potential futility of trying to identify every die pair - the "traditional" way of doing it in numismatics - in the face of such huge numbers and impenetrable gaps in the knowledge base.
So VAMming, by definition, doesn't necessarily lend itself to "complete" die pairing as does Sheldon or Overton. Yet, the great improvement in technology along with persistent years of research in the half-century since it all started have made it obvious we can see, identify and clearly illustrate the tiniest of die-made markers on any coin. So we're trying to nail all the die pairs possible.

Yet that's an ongoing process, and one where it's as necessary to make changes to past research - finding two VAMs are just different states of the same die pair, and getting them "officially" combined, for example - as it is to identify new combinations.
VAMming is
very much a work in progress, and I doubt our lifetimes will see the completion of the research. One must look at some of the fundamental suppositions regarding VAMs as moving targets, and be prepared to adjust one's own knowledge.