What Could Have Been: The series was pitched as a pretty straightforward action series of a hot mercenary who would hunt for treasure while battling armies. It was then revised to be the story of a fallen aristocrat heiress (Margaret assuming the codename MADLAX) surviving in a war torn world with her mechanic Elenore (eventually revised to be the maid) then made the eventual evolve to the Mind Screw plot of today.
Madlax deserves a mention just for the sheer faith Bee Train had that their audience would stick with them through anything after their success with Noir. The first two episodes look for all the world like they come from two completely different shows, it's not until episode seven that the two storylines explicitly cross over, and it's not until the final third of the show that the two protagonists actually meet. Plus, there's occasional asides with a weird looking girl and boy in an ethereal landscape that comment on the action and sometimes seem to talk directly to the audience, for which we get zero explanation until the last two episodes.
A lot of the the key plot points for Madlax were created while brainstorming drunk. Which explains a lot.
The ridiculous name 'Friday Monday' may in fact be a G. K. Chesterton reference—specifically, to The Man Who Was Thursday, which is about a group of alleged anarchists (in the philosophical rather than political sense) who use the days of the week as code names. Friday Monday and the Council of Days share similar philosophies and the ability to combine Narm and genuine nightmarish stuff.