We're playing in the Theban Tribunal (this is the Base Camp saga, at http://forum.atlas-games.com/viewforum.php?f=50), and my maga is looking for an apprentice. We're using a modified version of the canonical Theban system found in Sundered Eagle, pp. 32-34. I've noticed something odd, and probably unintended, about the system: the way it's written, a maga has a reasonable chance of seeking a single apprentice and ending up with two or more, almost by accident.
How? The book suggests it's normal to give tokens to more than one apprentice, which makes perfect sense, as a maga can't be guaranteed she's going to get her favorite. However, a consequence of this situation (with the apprentices deciding on masters after all "bids" are in) is that the number of apprentices a maga ends up with is rather unpredictable: a maga who gives tokens to two candidates could end up with one, two, or no apprentices. This unpredictability seems, to me, to be quite at odds with the orderly intent of the whole Theban process, especially since most magi don't want to try to train two apprentices at once, but yet it's risky to give tokens only to one candidate. (My maga, alas, can't plead this intent--due to a case of analysis paralysis, she's quite willing to end up with two of them.)
I see three possibilities for how the possibility of multiple apprentices works out in practice:
It works just as written, and it's not uncommon for a maga to end up with two new apprentices at once. As I said, this seems at odds with the intent of the system.
There are formal or informal mechanisms operated by the Tribunal or the individual magi that prevent this outcome, such as negotiations between potential masters (not unrealistic, but would probably be frowned upon as taking choice away from the apprentice candidates themselves), or an option for a maga chosen by two candidates to turn down one of them.
The apprentice candidates themselves work things out so that two of them aren't choosing the same maga. Of course, two of them who hit it off might actually want to be apprenticed together, or, if the order of candidate presentation matters, there might be some double-crossing, but it will be uncommon for one maga to end up with two apprentices.
I have been in situations where the PC covenant has found a Gifted child and not wanted to let nearby magi claim them (for one reason or another), so a magus ended up with two apprentices. Seeing as you have to spend one season a year training them, theoretically there's nothing against you training four at once if you really want to expand your house's numbers with no regards to your own magical development.
Last time I played in the Theban tribunal, the SG ran it as there being all sorts of informal behind-the-scenes chats to try and get the right apprentice, with magi hinting to each other about possible bidding wars. We had a situation where a covenant that was training apprentices (because one of their number had been assigned that duty at the previous Tribunal) had an apprentice who really wanted to stay with them, but they didn't think she'd be a good fit - however, they didn't want to offend her by not offering her a token. They asked us to make a higher offer and promised to lend us books from their library for the next 14 years (a standard Theban apprenticeship) if she accepted our offer. We duly offered three tokens to her and said we had a lovely covenant on a beautiful island bay. She took the offer of a single token from the covenant that only semi-wanted her, as she really wanted to stay there.
If you don't want to risk getting two at once, you need to either persuade other magi to favour your bid (by backing off from your favourite, or by making better offers to another one), or just make one bid and risk not getting the apprentice you want. There's always the possibility of their being apprentices that no-one of good standing has offered tokens to - you can then take your chances with all the shard-ridden villains of the Tribunal over the leftover apprentices.
The offer may be considered closed, formally or informally, once one apprentice has chosen. However consider that while an apprentice may file a complaint of abuse, a magus is allowed to sell their apprentices, or foster them out (perhaps they can be fostered on a rotating basis). Of course apprenticeship isn't formally begun until the arts are opened, and simply explaining to one apprentice the potential consequences of this choice may be enough to get them to reconsider...
Why not have the potential apprentices have a sort of contest to suss out who ends up being the true? Say you grant out tokens to 3 children, and you end up with all 3. As stated it takes a full season to train one (after opening the arts), so you get to explain to all three of them that, should you take them all on, someone is going to have to be first, someone is going to have to be second, and then someone is going to have to be last. This means that apprentice 1 is always going to be at least 2 full seasons ahead of the last one, and nobody wants that, do they? Of course not.
So set up a competition of some kind to determine which apprentice shall ultimately be chosen, with the remaining 2 sent back into the "pool" of apprentice candidates. Nothing nasty like fighting each other or dungeon delving. But perhaps something simple, like following the instructions to brew a potion, or rushing through the library on some kind of intellectual treasure hunt. First one to cross the finish line gets the prize?
Not to mention that, in theory, if you don't open their arts in the season after the Tribunal, someone else could claim them... or (given the Theban system) you could be charged with abuse of your apprentice and lose them.