How should a consultant extend access for an integration user that requires write permissions to a custom object?

Creating permission sets and groups to grant the necessary permissions is the most efficient and flexible way to extend access for an integration user requiring write permissions to a custom object. Permission sets are special Salesforce objects that provide additional permissions to users on top of their profiles. This allows for granular control, enabling the consultant to grant specific permissions without altering the user's entire profile.

By using permission sets, the consultant can easily manage and adjust permissions as needed without impacting the base profile of the integration user. This is especially useful in a dynamic environment where access requirements can change frequently. Additionally, grouping users under permission sets can streamline the process when multiple users require similar access.

Other methods like using a Salesforce administrator account for integration purposes introduce risks and are not advisable for security and accountability reasons. Modifying the integration user's profile could result in excessive permissions that may not be necessary for that user's functions. Assigning read-only permissions falls short since the question specifies the need for write permissions, making it unsuitable for the user’s requirements.