How do you remove one of the parties from a multi-party agreement?

The commentary (which generally assumes there are only two parties to a contract) generally draws a distinction between variation (in summary, where the terms of a contract are altered) and a contract for termination (or rescission) (where the contract is terminated). The consequences of a termination by agreement depend on the intention of the parties. For further information see: Termination, rescission and variation: Common Law Series: The Law of Contract [7.4] and Discharge by subsequent agreement: Halsbury's Laws of England [367]. For further information see: Variation: Halsbury's Laws of England [373] and Termination by agreement—Express