Respectfully disagree, controlling the internal and controlling bob are parallel at best, they are not binary states.
No one (other than possibly the sprinkling of humans who have achieved enlightenment or someone temporarily under a heavy dose of psycho-motor stimulants) can fully control themselves internally. Minor, fleeting internal control occurs frequently. Being able to sum up the strength to initiate the process of planning and acting to perform directed speech to control Bob would be an example of this (and appropriate for your additive example) but the full state of internal control required to disconnect your senses and observation from Bob's incoming external interferences without impacting your own faculties or performance is a rare kind, or 'level' of internal control that many do not possess. Interestingly, this is all derivative of personality.
They might be "parallel" if there were no zero-sum time trade off, or no time pressure. I wouldn't mind so much spending time fielding interrupts all day every day, if I didn't have anything else I was trying to get done. But that's not the reality. And for me (and I think many others), it isn't just additive, because time pressure makes me anxious and less focused, which slows me down more, which increases the time pressure, which makes me more anxious, etc.
By the way, I'm not trying to say that this is always happening in my work, or even frequently, but this is an actual bad outcome that I experience from time to time. I currently have, and have been fortunate in my career to usually have very good management and teammates who are very respectful of each other's focus time.
No one (other than possibly the sprinkling of humans who have achieved enlightenment or someone temporarily under a heavy dose of psycho-motor stimulants) can fully control themselves internally. Minor, fleeting internal control occurs frequently. Being able to sum up the strength to initiate the process of planning and acting to perform directed speech to control Bob would be an example of this (and appropriate for your additive example) but the full state of internal control required to disconnect your senses and observation from Bob's incoming external interferences without impacting your own faculties or performance is a rare kind, or 'level' of internal control that many do not possess. Interestingly, this is all derivative of personality.