Yes but it requires a fair bit of up front design work. I assume you mean enter new records and updating existing ones because updating is 'adding' data, yes? But what about deleting records?
In the least, you'd need a table of users, and for every table that you care about these changes, a field to tie back to that user. Knowing who doesn't tell you what or when, so that probably wouldn't be of much help. If you want to know when, that's not hard. To know what, you'd have to keep the original record for every delete/update.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.