Parties are free to modify their original agreement after it is made. A contract may be explained or supplemented by new agreements or the course of dealing. These modifications are at least amendments, and in some cases can completely preempt the old agreement.
Amendment of a contract takes place after the agreement. An amendment, like the original contract, occurs when the parties make a subsequent agreement. Unless the contract specifies that amendments can only be made a specific way (e.g., in writing signed by both parties), an amendment can be made in different ways.
In practice, this means that a contract can be changed by the parties without a new writing in a couple of different ways. First, if the parties actually perform the agreement in a manner different than specified by the terms of the contract, that course of dealing likely exhibits an agreement by the parties which supplants the terms in the contract. Second, the parties may discuss a change to which they agree orally or in practice, and that agreement may amend the original contract.
When a business has several people working together, amendments can take place by a person acting for the business. If the other party reasonably believes the business representative has authority to make a change, the change can be enforced, even if that representative did not have actual authority for the business to make the change. If that representative did not have authority, the business may have to live with the change, and its only recourse may be to hold the representative accountable.
When a contract does not specifically address how an amendment can occur, the business leaves itself open. If the right situation occurs, an amendment may have taken place. Disputes regarding these situations will be governed by looking at the evidence of that agreement outside of the terms of the contract.
However, a contract can include a couple of different terms that clarify how an amendment takes place, or what happens when the parties engage in a course of conduct different than the terms of the agreement.