SharePoint list threshold limit

[CirrusTech]

Hi 

We run an access database connected to SharePoint online lists. One of the lists has 16000 items and I need to add an additional field (type lookup) but when trying to add this get an error saying "the attempted operation is prohibited because it exceeds the list view threshold"

I can't seem to find a way to increase the 5000 threshold limit to get around this. Is the only option to removed items to get the limit under 5000 to then be able to add a field? 
(we can't create a new list and copy the data in as the autonumber ID from the existing list is used in the database)

Any suggestions would be appreciated!

[#2]

@CirrusTech 

SharePoint Lists can have 30 million objects (at the time of writing), the threshold is hard-coded for performance and can't be changed.

You shouldn't need to remove items to add a field, but limit the view by using filter should remove any errors when checking the list.