Frankly, none.
But some in here are trying to push the notion of Crosby having superior longevity of prime to Howe based entirely on the stretch of time where it could be argued either player was the best in the world. The flaws with this reasoning have been pointed out more than enough times by now.
At the end of the day, the OP asked if any player had a chance to break into the Big 4. Barring something extraordinary occurring, Crosby's chance has come and gone, and only the most selective of reasoning can place him on an equal footing with Howe or any of the others, at present or under any reasonable projection scenario.
At this point, I'd bet on McDavid breaking into that group long before I bet on Crosby. It's still entirely unknown what level he will achieve. His first three seasons compare pretty well with Lemieux's. Crosby's did too, but he never had the next level spike. The possibility exists that McDavid will.
You just used the key word "argued". Of course everything to do with rating players is an argument, especially when most of these players usually never played at the same time and/or in the exact same role and situation even if they did.
The OP was asking for a legitimate argument. Crosby has legitimately been in the conversation for the best player since 2006 if one chooses to look beyond assessing seasons individually and in a complete vacuum, and with reasonable consideration for partial seasons. Using the same metrics, Howe was the best player fro 50/51 to 63/64 IMO. Crosby has a chance to be in that position for a longer period of time. I understand that "Best Player" can be very subjective but I would argue that any argument against Crosby being the best/co-best at any time from 06/07 to 16/17 can be made against Howe, or any other player for that matter.
Does this mean the quality of prime is better? Nope
Does this lessen the gap in their peaks? Nope
Should it hold some value? I think it would make him the unanimous #5 player, and at least present a legitimate argument whether he did enough to be put on the same tier as the Big 4. If he can add to his playoff resume to be clear of Mario and Orr, and maybe Howe, then that would also significantly add to the argument.
Would he be close in peak to Orr, Wayne, and Mario? Nope but there are strong arguments that Howe, on peak alone, would not be in the Big 4. IMO, Howe has the 4th best RS peak but does not have a clear 4th best playoff peak, let alone one that is as statistically close to the other 3 as his RS peak is.
Would he have a "longevity" argument that, like Howe, makes up for perceived differences in peak? I don't see why not.
Would he have a resume that "outacheives" Mario's? I don't see why not since actual achievements usually place Mario 4th behind Howe who is usually viewed has not being on the same level talent-wise or peak-wise.
Would a playoff resume that matches or even betters Howe's add a significant second argument for inclusion with the Big 4? I don't see why not.
The narrative for Crosby would be a career that was spent at the very top of the league longer than any other player in history plus one of the best playoff resumes and/or peaks other than Wayne.