come on in

come in

1. To enter a place, such as a room, house, etc. Often used as an imperative. In this usage, "on" can be used between "come" and "in." I came in while the meeting was in progress, so I waited in the back. Come in! I'm in the kitchen! Come on in and have a seat.
2. To arrive at a particular place or destination. Those dresses were scheduled to come in last Tuesday. When does your flight come in?
3. To finish a contest or competition in a particular position or place (as in first, second, third, etc.). I didn't expect to come in first or anything, but finishing last is pretty disappointing.
4. To join something that is already in progress, often in a particular way or role. Ashley will sing the verse, and then we'll all come in on the chorus.
5. To be received, as of a transmission. Call me back later—you're not coming in well, so I can barely hear you.
6. To have or finish with a particular value or measurement. You came in at two minutes and 30 seconds, which is a better time than your last race. The estimate came in way too high, so we have to solicit more bids.
7. To approach or reach the shore, as of the tide. If you're trying to stay dry, we should move our chairs back before the tide comes in again.
8. To receive or be subject to something. Those boys are going to have to come in for a punishment after starting the food fight.
9. To join a group in doing something. We're pooling our money to get Sean a graduation gift, if you want to come in with us.
See also: come

come on in

A polite request or command to enter some place. Come on in, we've got a place at the table ready for you! Thank you for calling over, won't you please come on in?
See also: come, on
Farlex Dictionary of Idioms.

come on in

Please enter, as in Come on in, the door's open. This phrase is simply a friendly request to enter one's house or some other place. The related come on in, the water's fine originated as an encouragement (or, sometimes, a command) to a reluctant or fearful swimmer but has been extended to other activities, as in Come on in, the water's fine-this is a great office to work in!
See also: come, on
The American Heritage® Dictionary of Idioms by Christine Ammer.
See also:
  • come in
  • come in a certain position
  • empty in(to) (something)
  • empty into
  • be (flat) on (one's) back
  • (Is) that everything?
  • flat on (one's) back
  • flat on back
  • flat on one's back
  • a cold day in Hell