Import SQL data on an existing server

A client asked me to help them import MySQL analytics data over to a DB that already had data in it.

The main problem with a direct import is that most rows in MySQL have an auto-incrementing ID, so old data will have ID conflicts with the new data.

The solution I found was to add a large value (e.g. 10 million) to the rows in the new data, before importing the old one.

Is there a better solution for such cases?