I have a member signed up to the wrong event. I can't find a way to switch to the right event through the back end. I see Transfer - but it transfers to another person; not another event. Is it possible?
This is not possible via the UI.
There is a table civicrm_participant_payment which links the Participant and the Contribution records.
If you have access to that, and know the contribution_id then you should be able to edit participant_id
Alternative to the good suggestion by @petednz - fuzion would be to use the API explorer (see https://docs.civicrm.org/dev/en/latest/)