  General metric theories of gravity in four-dimensional spacetimes can contain
at most six polarization modes (two spin-0, two spin-1 and two spin-2) of
gravitational waves (GWs). It has been recently shown that, with using four GW
non-coaligned detectors, a direct test of the spin-1 modes can be done in
principle separately from the spin-0 and spin-2 modes for a GW source in
particular sky positions [Hagihara et al., Phys. Rev. D 98, 064035 (2018)].
They have found particular sky positions that satisfy a condition of killing
completely the spin-0 modes in a so-called null stream which is a linear
combination of the signal outputs to kill the spin-2 modes. The present paper
expands the method to discuss a possibility that the spin-0 modes are not
completely but effectively suppressed in the null streams to test the spin-1
modes separately from the other modes, especially with an expected network of
Advanced LIGO, Advanced Virgo and KAGRA. We study also a possibility that the
spin-1 modes are substantially suppressed in the null streams to test the
spin-0 modes separately from the other modes, though the spin-1 modes for any
sky position cannot be completely killed in the null streams. Moreover, we find
that the coefficient of the spin-0 modes in the null stream is significantly
small for the GW170817 event, so that an upper bound can be placed on the
amplitude of the spin-1 modes as $< 6 \times 10^{-23}$.
