  We present some computations of higher rank refined Donaldson-Thomas
invariants on local curve geometries, corresponding to local D6-D2-D0 or
D4-D2-D0 configurations. A refined wall-crossing formula for invariants with
higher D6 or D4 ranks is derived and verified to agree with the existing
formulas under the unrefined limit. Using the formula, refined invariants on
the $(-1,-1)$ and $(-2,0)$ local rational curve with higher D6 or D4 ranks are
computed.
