After composing an open-ended, debatable question, the next step to developing a well-supported, logical argument is to

identify the main issues regarding the topic.
determine the main arguments for and against the topic.
find various reliable resources with different perspectives about the topic.
take a stand on the issue and determine the right and wrong sides of the topic.

Answer:

After composing an open-ended, debatable question, the next step to developing a well-supported, logical argument is to C: find various reliable resources with different perspectives about the topic.

Explanation:

To develop a strong and logical argument, one should understand different perspectives of the topic. By understanding the opposing ideas of the topic, it will present a well-rounded and complete discussion on the topic.  

Ideas can be presented well. The listener would understand and believe in the topic as it has been studied critically and all the aspects have been considered.  

After analyzing different perspectives, conclusion can be reached giving a strong, logical argument to the topic.