What do you think of this argument for God?

[Nonpareil]

The real argument can be formulated as follows:

1- It is possible that a maximally great being exists.

Incoherent terms, bare assertion.

2- If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
3- If a maximally great being exists in some possible world, then it exists in every possible world.

Non sequitur.

A. The argument hangs on the concept of necessary (within premise 3)

The argument does not make use of the "necessary" concept.

Even if it did, it would remain nonsensical. A being that is possibly necessary in one world is not... well, necessarily necessary in other worlds, as there is possibly a world where it is not necessary.

This is why the modal ontological argument is such complete bunk; even granting that its definitions are coherent (and they aren't), it fails to establish that they actually apply.

While greatness might be subjective, maximal greatness is not.

Asserting this does not make it true. "Greatness" is still a value judgment. It is still subjective. Adding "maximal" to it does not make it any less so.