Use between in the introductory clause rather than amongst or a combination such as by and between. It subtly gives the agreement a more personal character, as is more consistent with the nature of contracts (i.e. reflecting the consent of two or more parties, rather than a mere bargain). Semantically, the distinction between between and amongst is not whether you refer to two parties or to three or more; it is whether you refer to one thing and another or to a collective or undefined number. Compare walk between two trees with walk among the trees.
Avoid using by for the same reason as applies to amongst; it turns an agreement into something outside the parties (i.e. the parties are the makers of a contract, being a work). Nevertheless, whether you use between or amongst does not influence the legal effect of the contract.