I've booked 4 to Europe often. BA seems to have the best avaiability, but the highest fuel charges. Stuff I have booked or seen and held or considered on *A or OW includes:
PHX-LHR, lots of ways. (Through Canada on AC, either direction. Via SFO, IAH or EWR on UA. Easier to find F for 4 than C sometimes. BA direct or LAS to LHR. F easier than C some days.)
LAX-MAD, IB C. (Great option with kids because it leaves at 6 pm. Long enough for dinner, movie and a good sleep.)
XXX-NYC/ORD-VIE/BRU (OS and SN, UA through EWR; lots of onward EU destinations from both cities on *A.)
PHX-PHL/CLT-CDG/MAD/BCN (US C; some CLT flights are not on the A330, so no lie flat).
In and out of FRA/MUC from all over.
BCN-FRA-PHL-PHX (LH & US in C. This was a tough get. Have it booked for the summer.)
BCN-MAD-ORD/JFK/BOS/MIA? (IB C)