For integrating a custom CRM system with Adobe Campaign Classic to push profile data, the two primary methods of HTTP communication available are SOAP and REST APIs.

SOAP (Simple Object Access Protocol):

Adobe Campaign Classic supports SOAP web services, which allow external systems to interact with Campaign's data and services. SOAP is well-suited for structured, reliable data exchanges, and Adobe Campaign provides extensive SOAP API documentation for operations such as creating, updating, and deleting profiles.

REST (Representational State Transfer):

Adobe Campaign also supports RESTful APIs, which provide a more lightweight and flexible way to interact with Campaign Classic. REST APIs are ideal for web-based integrations due to their simplicity and compatibility with JSON, making them a popular choice for modern applications.

Using SFTP would not meet the requirement of HTTP-based communication, and External Account is more about configuring connection settings rather than serving as a direct data transfer method. Therefore, SOAP and REST are the best methods to meet the integration requirements for the CRM system and Adobe Campaign Classic.