Do you mean maximum likely to be granted when deer is given as the good reason or maximum that you might get conditioned for deer once another good reason is established?
I can only repeat what others have said but a magnum .30cal is likely to be the upper end for deer where that is the good reason (although you might also manage something like the .35 Whelen, 9.3x62 etc as they aren't any more powerful).
However, I have heard go guys who have bigger things for boar, DG etc managing to convince their FEO to add the AOLQ condition so that they can use it for deer. The important distinction is that they wouldn't get that cartridge for deer if they had simply asked for a .375H&H on a variation and put 'deer' as good reason, they've established a good reason for the 'big' calibre and managed to have the condition opened.
In either case, you'll need to show the FEO you know what you are doing first, I don't suppose they will give a .300WM or add AOLQ for a DG rifle for a new/recent FAC grant.