Chimney flashing repair- one side only?

Our chimney is at the peak of our roof. Only one side of the flashing is leaking (as per extensive water testing). Can just one side be repaired? Or will the corners of the repaired side be prone to leaking where they meet the non repaired sides? Had multiple quotes and some roofers are saying you can repair one side only, some are saying you must do it the whole way around.