We present H-alpha velocity maps for the HIghMass galaxies UGC 7899, UGC8475, UGC 9037 and UGC 9334, obtained with the SITELLE Imaging FourierTransform Spectrometer on the Canada-France-Hawaii Telescope, to search forkinematic signatures of late gas accretion to explain their large atomic gasreservoirs. The maps for UGC 7899, UGC 9037, and UGC 9334 are amenable to diskwide radial flow searches with the DiskFit algorithm, and those for UGC 7899and UGC 9037 are also amenable to inner-disk kinematic analyses. We find noevidence for outer disk radial flows down to Vr ~ 20 km/s in UGC 9037 and UGC9334, but hints of such flows in UGC 7899. Conversely, we find clear signaturesof inner (r ~ 5 kpc) noncircularities in UGC 7899 and UGC 9037 that can bemodelled as either bisymmetric (which could be produced by a bar) or radialflows. Comparing these models to the structure implied by photometricdisk-bulge-bar decompositions, we favour inner radial flows in UGC 7899 and aninner bar in UGC 9037. With hints of outer disk radial flows and an outer diskwarp, UGC 7899 is the best candidate for late accretion among the galaxiesexamined, but additional modelling is required to disentangle potentialdegeneracies between these signatures in H I and H-alpha velocity maps. Oursearch provides only weak = constraints on hot-mode accretion models that couldexplain the unusually high H I content of HIghMass galaxies.