By 'at once' you mean with a single photon? I'd say no. It's never been done, for sure.
I wouldn't say it's absolutely impossible; there's probably some extremely-unlikely mechanism by which it might be able to occur by transferring momentum back-and-forth. (e.g. single-electron ionization followed by that electron falling back to the atom (somehow) and scattering while ionizing the second electron. Something like that.) But not directly, no.
I'd venture a guess saying that it is possible to ionize both electrons so close together that for all practical purposes you could say that it was at the same time. I don't believe the ionization energy would increase, but I can't say for sure.