Approximately 20, it depends on the time of day, how much sleep I have had the night before, and how well nourished I am. If conditions are favorable, I can rock and roll. If I'm tired, hungry, dehydrated, or hypothermic, I will still attempt to do as many tasks at once as before, but some items will fall out of my crosscheck and reduce my overall effectiveness.
Obviously I don't have 20 hands so I can't do all 20 things simultaneously, but I can switch rapidly between them while keeping awareness of the progress and situation of each particular task, as well as the changing priorities of the various tasks as the tactical situation evolves. In my profession, successful multitasking is an essential, perhaps critical, skill.