  Coupled frustrated spin-1/2 chains in high magnetic fields described within
the ferro- antiferromagnetic J1-J2 Heisenberg model are studied by the DMRG,
the hard core boson, and the spin wave theory approaches. Multipolar phases
related to magnon bound states are destroyed (supported) by weak
antiferromagnetic (ferromagnetic) interchain couplings Jic. We show that
quantum spin nematics might be found for LiVCuO4 whereas for Li(Na)Cu2O2 it is
prevented by a sizeable antiferromagnetic Jic. Also for Li2ZrCuO4 with a small
antiferromagnetic Jic expected triatic or quartic phases are unlikely, too. The
saturation field is found to be strongly affected even by a relatively small
Jic.
