I have a dedicated search layout set up with a multi-line text field for searching addresses. I unchecked, under field behavior, the options to go to the next field using return or the enter key.

In find mode, whenever the user hits enter in this field, instead of going to the next line, it submits the search and tries to "find."

I don't want that to happen because I have a button on the layout that should perform that function.

What do I have to do to make the enter key start a new line and not submit the search form?

The reason for this behavior is you can't create search criteria with a return character in it. Even if you enter find mode manually, you can't enter a return character. There is no way to override this behavior unless you enter your find criteria in a global field(s) in browse mode and then transfer the data to find mode with Set Field steps.

If you tell us more about your multi-line search needs and why you need them, we might be able to provide an alternative solution.