Most airlines offer RTW with other airlines other than their own alliances. Sometimes you can get one alliance member team up with another to have a joint round the world. For example: CX/UA, CX/DL, CX/TW. Or SQ/KL, SQ/TW or NW/VS, KL/AN/NZ.

The most important fact to you is what are your cities, and the airlines you want to fly with. Then the frequent flyer programmes kick in.