We use come to describe movement between the speaker and listener, and movement from another place to the place where the speaker or listener is. We usually use go to talk about movement from where the speaker or listener is to another place. When we talk about another person (someone who is neither the speaker nor the listener), we can use either come or go, depending on whether the speaker sees things from the receiver’s viewpoint (come) or the doer’s viewpoint (go). [doer] Yolanda came to [receiver] her mother for help. We use come when we see things from the receiver’s viewpoint (in this case the mother). [doer] Melissa went to [receiver] her mother for help. We use go when we see things from the doer’s viewpoint (in this case Melissa). This is taken from the Cambridge Dictionary. So using this explanation ( which I agree with as a native English speaker whose English is derived from Britain), I would say, " Can I come your office tomorrow" I say this because I am the speaker travelling to the listener's office. However, If I ( the attorney) am speaking to the listener( a client) and we need to travel to someone else's office ( the real estate agent) I would then say, " We need to go to Peter's office tomorrow at 900 am for our meeting". Peter if he spoke to either me or my client would then say, " Please come to my office at 900am tomorrow" I hope this clears it up for you.

Both are correct. Which one you choose to use depends on the picture you have in your own mind. Do you imagine yourself arriving at the office, or do you imagine yourself leaving where you are to go to the office? I prefer "can I come" because it is more empathetic - you are looking at things from the point of view of the other person because you will be "coming" TO THEM. If you say "can I go to", you are looking at it more from your own point of view because you will be leaving the place where YOU are. It seems more polite to me to say "can I come", but the distinction is not important.

Native English speaker here and I would also say both are correct. For example: Can I come over to your house? Can we go to the movies tomorrow? Let's go to the park on Wednesday. Come to work prepared next time. I know. Confusing hahaha If you are looking for an English teacher, I teach kids and adults of all levels and ages. I've taught over 6000 classes since 2018. See you soon.

For my part, they are both natural, but it depends on your context and situations.

I would definitely try to remember what Nanren888- 新西兰 explained. Unfortunately, I have to admit that the majority of American English speakers use these two words, "come" and "go" incorrectly and you will hear most of us say, "Can I come to your office tomorrow?" even if the situation doesn't fit its use. We rarely are corrected when we make this mistake and since we all understand one another, we ignore it.