Well conservatively assuming that each galaxy supports lives at 10^9 per sun per century (1/10th of our solar system), that's already 10^29 lives per second right there.

And assuming utilization of all the output of the sun for living, i.e. some kind of giant spherical shell of habitable land, we can add another 12 orders of magnitude straight away. Then if we upload people that's probably another 10 orders of magnitude.

Probably up to 10^50 lives per second, without assuming any new physics could be discovered (a dubious assumption). If instead we assume that quantum gravity gives us as much of an increase in power as going from newtonian physics to quantum mechanics did, we can pretty much slap another 20 orders of magnitude onto it, with some small probability of the answer being "infinity".

Now thats a way to eat up your brain.