In the UK, it's certainly worth trying. Apart from purely the fact that places may prefer to keep you for 4 days rather than lose you, employees have the right to request part time work (amongst other things). Businesses have to give a reason if they say no, and the reasons get harder to justify typically as a business grows. Not guaranteed, of course, that would be rough on all businesses but it's certainly something that should be taken seriously.
It won't be publicly broadcast, but if you ask around it is an option.