A general formalism is presented for the calculation of simultaneous electron-impact ionization-excitation in a model that accounts for interactions up to second order of the projectile electron with the target, in combination with a convergent R-matrix with pseudo-states (RMPS) model to describe the initial target state and the ejected-electron-residual-ion interaction. Example results for ionization-excitation of helium to the He+(n= 2) states show qualitative agreement with the recent predictions of Marchalant et al (1999 J. Phys. B: At. Mol. Opt. Phys. 32 L705), but also indicate that the latter results are likely to change substantially if the calculation of the second-order term were improved. Despite some remaining discrepancies, the overall agreement with the available experimental data is very satisfactory, indicating that our model contains the most important physics and is numerically converged.