This is a helpful Medscape diagram showing causes of direct-antiglobulin-test-positive hemolytic anemias. Note that not all cases of the conditions may consistently be DAT-positive, especially the ones that fix complement. Again, a negative result means non-detected, not necessarily not present.
In my own test algorithm, if hemolysis is suspected, I would perform monospecific IgG and C3 DATs. I might also include a special DAT card detecting both C3c and C3d and heavy-chains mu (IgM) and alpha (IgA) if the initial DAT is negative. C3c positivity would tell me that active complement activation is occurring.