  We calculate two-photon exchange (TPE) amplitudes for the elastic
electron-proton scattering, and take into account intermediate hadronic states
containing \pi N system with total angular momentum 1/2 or 3/2, which includes
8 different channels. This is the improvement of our previous calculation,
where only the \pi N states with quantum numbers of \Delta(1232) resonance were
included. The results show good consistency with recent experimental data. At
high Q^2, newly-calculated contributions affect the correction to the measured
proton form factor ratio \mu G_E/G_M. The total correction becomes somewhat
smaller compared to our previous work, but is still significant and grows
approximately linearly with Q^2. Comparing contributions of different channels,
we found that larger contributions come from the channels with quantum numbers
of lightest resonances.
