Ignoring the fact that "theoretical maximum" goes right up to "they conquer the whole world just by being lucky again and again", I'd say that a long-lasting Crusader state holding the Levant isn't at all outside the real of the plausible. It does require fundamental changes to what occurred in OTL. The main requirement for viability is "no unnecessary conflict with Constantinople". The splendid timeline
And All Nations Shall Gather To It by
@Rdffigueira given a very good portrayal of what that would look like (in the early stages).
As I have mentioned in that TL's discussion thread, in the longer term, the Crusaders will only be able to exploit their better strategic position (thanks to more firm alliance with the ERE) if they solve their manpower problem. One way to do that is thanks to butterflies (the greater success of the Crusades attracts more people to try their luck over there). Another is to craft the TL so that less fruitful crusading ventures of OTL are never embarked upon and the energy and manpower goes to more useful campaigns instead
The third (and most important) way is to have the Crusaders realise that they will need at least a portion of the locals to like/accept their rule-- and then to act accordigly. This would, I imagine, involve creating a society where anyone who converts to Catholicism is accepted into the higher strata of society, while other Christians are second-class citizens, but still above Jews, Muslims and Druze, who would be the lowest classes with few to no options to climb the social ladder. Such an approach, though hardly enlightened, would further conversion rates (since conversion opens a lot of doors for you that otherwise stay closed: conversion to Catholicism would be, for many people, the only realistic method of acquiring upward mobility. This may suggest that the people belonging to the 'bottom' group may be most interested in converting to Catholicism, since they have it the worst as long as they don't, and conversely have the most to gain from it if they do. (I have also suggested that certain groups, such as the Druze, could get a special place in the social order by becoming particularly trusted or high-valued auxiliaries. It wouldn't be the first time in history that we see such a thing.)
If such developments were to occur in an ATL scenario, I find it very realistic that the ATL Crusader state and the ERE could fight side by side to their mutual benefit, and succeed in 'holding the line' against any invasion attempts.
When we speak of what's
possible, however, we can go a bit beyond the aforementioned. It is far less certain that what I have already outlined, but given that same premise, a successful Crusader conquest of Egypt is hardly out of the question. As far as truly long-term strategy is concerned, I'd say that Egypt is indeed the logical target after you get your core territory secured. The reason simply being that controlling Egypt allows you to cut off (effective) trade between the (Islamic) East and (also Islamic) North Africa. Considering the substantial percentage of the Egyptian population that was still Coptic-Christian back in the day (a matter also discussed in the thread dedicated to the TL I linked above), Crusaders willing to treat the Copts with respect could find that Egypt can be added to their permanent holdings without any difficulty greater than that they'd encountered in the Levant.
In the case of both the Levant and Egypt, I can see the social pressures that would be at work there slowly working to whittle away the Muslim population to a rather slight minority, with no perspectives for re-asserting dominance. Or in other words: I think that in such an ATL as I have outlined here, there would by the present day be no more Muslims (percentage-wise) in the Crusader territories than there are Christians in Egypt in OTL. I can also see the Crusaders extending an olive branch and a proposal of mutual support to Christians to Egypt's south (Ethiopia!), to ensure that Islamic North Africa is well and truly cut off from Islamic Asia by a firm Christian 'wedge'. All this would greatly strengthen the position of Christendom vis-à-vis the Islamic World.
Now to get a bit more speculative. We may assume that these ATL Crusade gongs-on neither would nor should meaningfully affect the Reconquista of the Iberian peninsula. Which leaves us with an amalgamation of Christian realms that has, in essence, "locked its jaws" around the still-Islamic parts of North Africa. Those parts of North Africa are also, as suggested above, cut off from any meaningful support from the Islamic East. And historically, manpower was a serious issue for not just the Crusaders... but also for the polities of Islamic North Africa (and North Africa in general; Carthage already faced the same issue back in the day).
Based on such considerations, the most ambitious long-term goal of the encompassing "Crusading venture" then becomes quite clear: a Reconquista of all of North Africa. (By which I do not mean to say that this would be somehow easy, but rather that it would be the logical ambition, and could indeed happen -- in the long term -- if enough effort is dedicated to it.) This seems like a more realistic 'grand plan' than driving into Mesopotamia (which would be difficult to do and even more difficult to hold for the Crusaders), and also more sensible to a European mind (because a reconquista of North Africa would end Islamic piracy and restore the Mare Nostrum within the context of Christendom).
I think that just about sums up the ultimate bounds of what the Crusades could maximally accomplish-- and which can realistically ensue from the scenario I have suggested, if given enough time and a (still realistic) amount of good luck, with any truly implausable amounts of Crusader-wanking going on. All in all, this whole venture would immensely strengthen Christendom. This may cause further Christian victories over Muslim rivals (for instance, I could see follow-up campaigns in Armenia), but I won't include those matters here-- since I do not think that at that point we'll still be looking at "Crusades".