Student or Learner
Do you think the "over" in "Come over here" makes a difference in nuance?
For example, Are you more likely to use "Come over here" when you tell someone who is far away from you to come to you?
An unadorned "come here" can be interpreted as a command, and therefore might be offensive in some circumstances. In my opinion adding "over" softens the tone and avoids giving offense. Also, in casual AmE people say "come over here" or just "come over" when they want to invite someone to come to their home.