  In this paper we revisit potential biases in cosmic shear power spectra
caused by bias terms that multiply up to quadratic powers of the shear.
Expanding the multiplicative bias field as a series of independent spin-$s$
fields we find terms $m_s$ that multiply integer and half-integer powers of the
shear. We propagate these biases into shape measurement statistics and the
cosmic shear power spectrum. We find that such biases can be measured by
performing regression on calibration data. We find that for integer powers of
shear the impact of quadratic order terms on the power spectrum is an
additional bispectrum dependency; ignoring quadratic terms can lead to biases
in cosmological parameters of up to $2(m_2+m_{-2}-m_6)0.4\sigma$ for Stage-IV
dark energy experiments, but that the susceptibility to them can be decreased
by using methods to remove small-scale sensitivity. We also find, for
half-integer powers of the shear that, for a Stage-IV experiment, biases are
required to be known to better than approximately
$\sigma[m_0+15(m_1+m_3)+0.1(m_{-1}+m_5)]\leq 0.01$. In future, Stage-IV dark
energy experiments should seek to measure and minimise such all such bias
terms.
