Well, I'm doing silly things like thinking about rules additions/modifications before I've even played the game.. Excuse me if I say something that is said in a part of the rules I haven't read or that contradicts something, but here goes.
Quintessence isn't really explained in the game, just that it's what you use to cast arcane variants. As I see it, there are a few possible explanations to what quintessence is and why you can only channel a given amount of it before resting.
Possibility one. Quintessence is something you have within yourself. You can only draw it from yourself, and the QP a character has simply says how much of it naturally gets stored in your body. But what if QP is actually life force? Maybe the Dominion skill represents the art of training your body to store more Quintessence than what it actually uses to just live? Maybe a magician could draw more power from his body, at great pain and the risk of death if he draws too much?
A possible rule for this, would be that when a character has used up his QP, he can still cast spells at a cost of two LP per level. (Two could be changed to whatever depending on preference and game balance.)
Another possibility. Quintessence comes from outside yourself. It exist all around you, in nature, or maybe it comes from another dimension or plane of existence. Whatever. A character's QP in this case would be how much he can safely channel. Dominion would represent how much the character is in tune with the universe, or something like that.
"Safely channel"? you ask. Well, he can draw as much as he wants. Or at least try to draw it. If he passes a threshold decided by his attunement with nature (i.e. his QP), weird things begin to happen. Low levels of weirdness will just be inconvenient for the wizard, but higher levels might be deadly for himself and those around him!
Rules for this could go like this: Keep track of how QP the character has used. Once the total amount goes over the character's QP, you start rolling on a table with different effects (depending on the tone of your campaign). The total amount of QP should be added to every roll on the table, so even small spells could cause major backlashes to a magic user who has used lots of magic in a short time.
This option could alter the feel of a campaign quite much, but if you would decide to go with it, you might want to read for inspiration.
Well, a couple of ideas that might be fun to try out!