I can see no reason for any Amberite to have a limit on the number of spells in their spellbook.
I’ll use one of my own characters, Beatrice, as an example here.
Suppose she learned sorcery, as advanced as she was able to get at the time, by the age of 20. She had a small set of spells – say, 12.
Suppose she’s 50 now.
What was she doing in the intervening 30 years? Anything but sorcery? Even if you suppose it takes years to research any given spell, she ought to have more than she started with.
Suppose she reaches 100, takes the Pattern, studies until she has Advanced, and learns how to hang spells on the Pattern and incorporate it into her magic. She’s going to have more than 12 by then, surely!
Suppose she reaches 1,000. Does it make any sense for her to still only have 12 spells? Not even a little.
Now, why did I start with 12? Mostly because it was a nice round number, to be honest. A given character could start with 1 spell, or 1,000. A lot will depend on who taught them – a character learning sorcery mid-game should, to my mind, have most (if not all) of their starting spellbook in common with their teacher. I’d ask the player who their tutor is, and sit down with that player (if applicable) to go over their spellbook and find out what they might be willing to teach. Then I’d sit down with that list and the potential sorcerer and let them choose as many as they wanted off that list. This supposes, of course, that the teacher’s and student’s players are reasonable and don’t have any reason to screw each other over out of character.
In the end, I don’t care if a character starts with 1 spell or 100 as long as it’s reasonable that they’ve researched or learned that many in the time they’ve been alive. Where I’m concerned is the number of spells a character has racked, and that the spells that character does know are of reasonable power level.
(For the record – at 50, Beatrice had 31 spells. 
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