I am not familiar with the expression, 'limited free will', but I can see a sense in which it could be used.
The so-called libertarian view holds that X is free (has free will) at time t1 if and only if for some event or set of events, E2, there is no event or set of events, E1, that precedes E2 and is causally sufficient for E2. For 'events' we can read 'actions', which are a type of event.
In other words and in more detail, at time t1 for those actions in respect of which X is free, whatever the laws of nature and whatever the conditions of action, X can do simply any action that X chooses - and (a) X's choice, C1, itself is such that there is no event or set of events, E3, that precedes C1 and is causally sufficient for C1 and (b) X's action results from X's choice.
One might properly call this unlimited free will. (I offer no opinion as to its existence.)
In contrast, limited free will would take constraining factors into account in this sort of way :
At time t1, X could have chosen otherwise, C2, if X's desires and character had been different.
This leave's the agent's choice as the vital element but constrains that choice by the state of the agent's character and desires. One might in this case say that the agent had limited free will.
I am trying to conduct a purely conceptual exercise. What I think about free will - its reality or limits - cannot be inferred from anything here.
Reply
The objection, perfectly interesting, has been made :
Wouldn’t it be more appropriate to say the first example is an unlimited will which is truly free, whereas the second example is a limited will but in no way free? Or are unlimited and unrestricted not good synonyms for free in this context?
I find free will too tricky a topic to be dogmatic about but I'm inclined to reply that I think a choice limited by one's own desires and character is free; after all, one may have a range of choices given one's character and desires. It is not as if, given one's character and desires, there is only one possible choice. Given my character and desires, I may have choices 1, 2, 3 .... n. The actual choice I make is not determined by my character and desires, which merely set limits to the choices I can make.