The Laser Interferometer Space Antenna (LISA) will observe massive black hole binaries (MBHBs) with astoundingly high signal-to-noise ratio, leaving parameter estimation with these signals susceptible to seemingly small waveform errors. Of particular concern for MBHBs are errors due to neglected higher-order modes. We extend Yi et al. [Phys. Rev. D 112, 124063 (2025)] to examine errors due to neglected higher-order modes for MBHBs with nonzero (aligned) progenitor spins and total mass up to ${10}^8{M}_{\odot }$. For these very massive systems, there can be regions of parameter space in which the $(\ell ,|m|)=(2,2)$ modes are no longer dominant with respect to higher-order ones. We find that the extent of systematic bias can change significantly when varying the progenitor spins of the binary. We also find that for the heaviest, and therefore shortest, MBHB signals, slight systematic errors can cause severe misinference of the sky localization parameters. We propose an improved likelihood optimization scheme with respect to previous work as a way to predict these effects in a computationally efficient manner.

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