NEC ECC: Can CE's be issued by a Contractor or PM when the Completion Date has passed and the Contractor was late?

The Contractor is currently late and is being charged delay damages. The Contractor was suppose to complete by 30 September 2019. Their planned completion is 30 May 2020.

Can the Contractor/PM notify CE’s whilst the Contractor is being charged delay damages and is late.

Yes of course. The initial delay may well be Contractor liability, but there could be a further delay that moves planned Completion by say two weeks. That means they can claim the cost of that two week delay, but also move Completion Date by two weeks so they are no worse off or better off before and after the compensation event.

The compensation event process does not change just because the Contractor is already in delay.