Parfit characterizes the core issue as follows:
We are asking whether, in our thoughts about our lives and other features of the world, it is enough to think only about what actually happens or will happen.
I agree with Parfit that good practical reasoning often requires us to consider counterfactual possibilities. I'm not aware of anyone who disputes this. Metaphysical Actualists do not deny that we often need to consider non-actual possibilities. What they deny is that the concreta which would exist, were such a possibility actualized, thereby do exist in any strict or literal sense. [See Karen Bennett's non-domain-inclusive view in 'Two Axes of Actualism'.] Possibilists see "possibly existing" as a - perhaps lesser - way of existing. (As Parfit later writes, "Actual suffering exists in a thick ontological sense, and merely possible suffering exists in a much thinner sense." This makes it sound like a mere difference of degree.) This is what Actualists deny. A merely possible ham sandwich is, strictly speaking, no ham sandwich at all.
Parfit's objections to Actualism look horrendously question-begging. For example:
Actualists should admit that some things happen, and these things are events. If we could have acted differently, this event was not actual, but was merely possible. Since Actualists deny that there are any such events, their view implies that we could never have acted differently.
To say that we could have acted differently is to say, more broadly, that there could have occurred a different event from the one that actually occurred. Actualists can make such claims. (Actualism does not imply that there are no other ways things could have turned out!) We do not need to further claim that there is a particular non-actual event which is the one that would have occurred. Such reification -- promoting the existential quantifier out of the scope of the modal operator -- is a further, unnecessary move.
Possibilists happen to think that we can freely reify modal claims in this way. For the possibilist, whenever you have a claim like "Possibly, an F is G", we can say that there is some particular (perhaps non-actual) entity that the modal claim is referring to: the possible G. But the (non-domain-inclusive) Actualist denies this reifying move. They think that we can represent (de dicto) that an F is G, without there being any such objects to which we might refer (de re).
So it's clearly illegitimate for Parfit to argue against Actualism on the grounds that, by denying the permissive ontological claim that there are any non-actual persons or events, it is somehow committed to the restrictive modal claim that there couldn't have been different people or events. That would only follow if we assumed the truth of possibilism from the start!
Still, insofar as Parfit's real concerns are more practical than ontological, I think the standard Actualist view can give him all he wants. As I explain in my old post on 'Reifying Possibilia', we can talk loosely about mere possibilia, so long as we're more cautious when it comes to drawing metaphysical conclusions. And all that Parfit wants to establish is that there is "some sense" in which we can speak of there being mere possibilia. Actualism can provide this. We can say that "there is a possible X" in the loose sense when, really and strictly speaking, there could have been an X.
Would this move satisfy Parfit? Consider the following explanation of what he takes himself to be committed to in making claims like, "there is a possible child whom Sarah might have, but this child will never actually exist":
These claims would all be about the possible event in which Sarah has this child, and would tell us that this possible event will not occur, so that this possible child will not exist. To defend Actualism, we would have to defend the claim that
(W) it is in no sense true that there is such a possible event, and such a possible child whom Sarah might have.
On my version of metaphysical actualism, we do not need to defend that claim which Parfit considers indefensible. We can agree with him that in the loose sense there is a possible child whom Sarah might have. This is true in the sense that Sarah's having a child is a way the world could've been. (There is a maximal property or world-state that the world could - but does not - instantiate, such that if the world had been that way then the thought we now express with 'Sarah has a child' would have been true.) If this is all Parfit wants, then his Possibilism is compatible with Metaphysical Actualism.
A metaphysical possibilist would further insist that these modal claims are not just about qualitatively describable possibilities, but are about particular possible individuals. The possibilist thinks that the phrase "Sarah's merely possible child" picks out a particular being, in much the same way that "the author I'm arguing against" picks out Parfit. The metaphysical actualist, by contrast, denies that there is any such merely possible child to pick out. All that we can talk about is the world-state that could've been, but isn't actually, concretely realized.
Parfit's final concern is that actualism will lead us to neglect the possibility of improving the world by bringing more good lives into existence:
If there was no sense in which there ever are such [merely possible] people, it couldn't be true that we ought to think about what might have happened to such people.
It's true that we can't coherently regret the non-existence of merely possible people for their sakes. But so long as we reject the person-affecting view of normative reasons, we may still regret that the world is not as good as it would be if things turned out differently. So this is not a problem either.