Greece and Turkey can be reached on AA/BA with a transfer at LHR or via UA/LH/TK. It will all depend on the availability for the dates you are traveling.

For South America, AA or LAN will take you there with a connection in DFW/MIA.

Getting to South Africa, the best way would be to use UA miles to fly on South African Airways, although with AA/BA you can route through LHR once again.

To get to Morocco, I would use AA miles to fly AA/BA/IB and then connect at LHR or MAD to get there.

As for Thailand, you can go with AA/CX/JL to get there or a lot of options with UA miles whether flying with UA directly or with TG/NH/OZ.