Can I see him please, Mrs. Williams? = May I see him please? kinda, technically it is more correct to say "may i see him" because "can" is asking about the physical ability to see him, where as may is asking permission. However many native speakers ignore that rule very often so in everyday English the same meaning will come across. May I see him please? = check up on him please? May I see him please? = Can I check on him please? for both of these you are adding a bit of detail but they are essentially the same however, Can I check up on him please? is not exactly the same as Can I check on him please? can I check up on him feels like he is asking to get more information, can i check on him please feels like he has most of the information he needs and just wants to make sure everything is still going as expected. Certainly, doctor. Come upstairs. = Certainly, doctor. GO upstairs. = Certainly, doctor. WALK upstairs. = Certainly, doctor. COME UP THE STAIRS. ? come upstairs would be said if Mrs. Williams was upstairs talking to the doctor downstairs, go upstairs would be said if she was downstairs with him, for both of these you would want to soften the language a bit so it doesn't sound like an order I.E "Certainly, doctor. Just come upstairs." or what would probably be said is "Certainly, doctor. he is just upstairs" (implying the doctor should go upstairs but not telling him what to do). both "Certainly, doctor. WALK upstairs." & "Certainly, doctor. COME UP THE STAIRS." while technically correct would rarely be said as they both sound a bit odd.