I once ran a Vampire Troupe Game (Troupe means that it was disconnected from any other LARP games in the World of Darkness) which began with about 15 players who were either disgruntled with the Camarilla LARP or simply wanted an additional and different Vampire LARP game to supplement their gaming experience. Over time, I gained and lost players although as my pool of potential new players was quite low, I ended up with about six players before I cancelled the game.
Anyway, in this game I allowed players to have up to three characters and this had a number of benefits and drawbacks. It's really up to you in your LARP game as a Storyteller, or even as a Player, to decide which one is more problematic than the other.
MULTIPLE CHARACTERS PER PLAYER
Helps fill the gaps in court positions.
If you're bored, or have nothing to do that session, you can swap to a different character.
Gives you very different experiences and perspectives of the game and the characters within it.
It can create amusing situations where both your characters dislike each other (generally a good idea to help maintain distinction).
Those situations are all the more amusing if you're skilled at holding conversations with yourself (I've seen two characters played by the same player end up in a scuffle).
It helps fill out the clans and covenants so that no one is alone in any one covenant.
Multiple characters provide multiple plot threads and thus gives the game greater momentum.
Multiple characters provide more motivations for people to play around with.
Someone is bound to need to speak to a character othan than the one you are playing at the time.
Multiple positions can create a conflict of interest.
You will likely end up in the awkward position of knowing plots against your own character.
It is tricky to maintain boundaries between character knowledge as you may forget who knows what.
In attempting to keep in character knowledge separate, you might not realise that you really do have enough information for another character to figure it out.
Other players won't know where you got your information from or why you behaved the way you did and therefore may suspect cheating.
You'll need to divide game time between the various characters.
Both characters may be required to attend the same session at the same time.
A situation may arise where both characters may need to deal with each other.
In the end, my recommendations would be that very political LARP games limit characters to one per player as a player's perspective will colour the character's perspective. Since characters also do the same to players, there is a good chance that all of the characters will come to a similar opinion of another person's character. Sure, one might hate them, one might dislike them, and one might ignore them, but it's rare that one character will love them, another dislike them, and the third ignore them. In a plot-based LARP game, multiple characters per player can make it easier to provide hooks into the game as you can always request they play a character that would work well in the plot.
So there you have it. I hope that helps give you some perspective on this conundrum. Anyone else played in a LARP where there were multiple characters per player? Did you love it? Loathe it? How'd that work out for you?