I was mildly surprised to find that I’ve apparently never written anything on this blog about which to use, between or among, when listing the parties to a contract, in the introductory clause or elsewhere. Here’s what MSCD 2.46–48 has to say:
In all cases, use between as the preposition in the introductory clause rather than among or a silly couplet (see 1.42) such as by and between.
It’s commonly held that whereas one speaks of a contract between two parties, the correct preposition to use in the case of a contract involving more than two parties is among. But according to The Oxford English Dictionary, it’s not only permissible but actually preferable to use between rather than among with more than two parties. That the pointless distinction between between and among is generally accepted is a good indication of the state of traditional contract language.
That said, whether you use between or among has no effect on meaning or readability, so it would be unhelpful to make an issue of it. Use between in your drafts. If a traditionalist insists on among because there are more than two parties, agreeing to make that change would be a painless concession. If the other side presents you with a draft that uses among, asking that it be changed to between would likely antagonize them.
If you think that between versus among is a worthwhile use of anyone’s time, you’re in severe need of reindoctrination. Please present yourself at 14 Five Bells Lane, Nether Wallop, Hampshire, England, with a tin-foil hat on your head, ring the doorbell, and say, “I’m here to learn about active drafting.”