The question of whose bloodline will be chosen as dominant can be
answered simply by taking the highest score. However just because that
particular bloodline is dominant does not mean that the original
bloodline is displaced. They are simply both there. In my campaigns I
would say that getting married is a suitable way to add to your line.
For example: Ruinil(An, 35 Major) marries Jasmine (Ba, 27, Major)
Ruinil would be considered a member of both lines almost like noble
houses. The same would go for Jasmine she would be a member of the line
of Ruinil as well as her own but Ruinil's would be dominant. In my
campaigns it thus makes it very hard to get the 1 for 5 that you get if
you kill the last of the line. This example naturally only applies to
blooded scions and regents.