  We calculate the beam ($B_n$) and target ($A_n$) normal single-spin
asymmetries in electron-proton elastic scattering from two-photon exchange
amplitudes with resonance intermediate states of spin-parity $1/2^\pm$ and
$3/2^\pm$ and mass $W \lesssim 1.8$ GeV. The latest CLAS exclusive meson
electroproduction data are used as input for the transition amplitudes from the
proton to the excited resonance states. For $B_n$, the spin 3/2 resonances
dominate by an order of magnitude over the spin 1/2 states. In general we
observe cancellations between the negative contributions of the $\Delta(1232)$
and $N(1520)$ across both beam energy and scattering angle, and the positive
contributions of the $\Delta(1700)$ and $N(1720)$, leading to a rather large
overall uncertainty band in the total $B_n$. At forward angles and beam
energies $E_\textrm{lab}<1$ GeV, where the $\Delta(1232)$ dominates, the
calculated $B_n$ tend to overshoot the A4 and SAMPLE data. The calculated $B_n$
compare well with the measured values from the A4 and $Q_{\textrm{weak}}$
experiments with $E_\textrm{lab}>1$ GeV.
