No, the data from one AppleID will replace what is already there. If you sign out of your iCloud account and sign into theirs, their data will replace your on the device.
Also so note that if you sign into the App, iBook or iTunes stores with another AppleID, you may not be able to change it back to the original AppleID for up to 90 days (there is a timeout period to deter people sharing purchased content with others).
Why do you want to change the AppleIDs? Doing so can cause loss of data on one or both, or corrupting/merging data, unless you’re very careful. Ideally, you should sign out of everything (icloud, FaceTime, iMessage, all stores) then backup, then completely erase any iOS device before using a different AppleID with it so you don’t mess up the data associated with each AppleID.