How to form a cfhttp call to consume a custom webservice API?

Going to take your word and assume cannot do it with CF because as @Henry pointed out it's SOAP 1.2. So looks like this requires using Java directly, specifically Soap with Attachments API for Java (SAAJ). This is in the java package javax.xml. Soap which is not part of a standard Java distribution.

Instead it's a separate download from Oracle.

The easiest way is to create Java stubs for your webservice then creating a java object and making calls to java object in coldfusion.

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