Conversation so far:
What is intentionality for John Searle?
In Intentionality: An Essay in the Philosophy of Mind (1983), Searle applies the principles of his account(s) of illocutionary acts to the investigation of intentionality
Are there any other interesting aspects about the John Searle article?
Searle also introduces a technical term the Background, which, according to him, has been the source of much philosophical discussion.
What does the background mean for John Searle?
He calls Background the set of abilities, capacities, tendencies, and dispositions that humans have that are not themselves intentional states but that generate appropriate such states on demand.
What is the network for John Searle?
Searle supplements his reference to Background with the concept of the Network, one's network of other beliefs, desires, and other intentional states for any particular intentional state to make sense.

Question: What else did he believe?
Self-contained rewrite: What else did John Searle believe besides the Network?