I always fix my queries to be one-way and only the routes that I know the partner flies. For example, if you choose one-way, JFK - HKG, First, for Oct. 1, for one passenger, click continue through no stopover, click search for partner airlines, and then when nothing is found on Oct 1, click Search up to 7 days later, the website will then return availability on CX 841 on Oct 6. If I'm interested in a routing in F with a stopover in HKG, I piece it together one segment at a time, and then call BA when I've found the dates I'm happy with.....