Coming up with as many ideas as possible

Try ideation. Ideation is about generating many ideas without being hindered by creative, intellectual, or emotional constraints. You can ideate through brainstorming, mindmapping, co-creation, and more. For more, see Interaction Design Foundation on ideation.
Also see our talk-back boards recipe. This asynchronous research method allows users to write their answers to a question, which allows you to crowdsource the ideation process.