NEC4 ECC Option C: Correction to a previously implemented CE

I have implemented a compensation event recently for additional work carried out by the Contractor, in which I had not included any assumptions about the quotation.
The quotation was submitted and, having discussed that with the Contractor, I made my own assessment which is much lower that the Contractor’s quotation.
(the contractor has undertaken a large survey, the results of which have been interpreted to forecast the quantity of work in the next stage in the process - design).
The Contractor made a number of assumptions in its forecast which I disagreed with. Therefore I made my own assessment.
We have discussed this at length to understand the fundamental differences in our assessments and we have identified some assumptions which, had I included them in my instruction to provide a quotation, could have been used by the Contractor and may have aligned our assessments a little closer.
I know that the original CE cannot be revised, but would it be possible to notify another CE including some of the assumptions which would give the Contractor an opportunity later in the project to notify under 60.1(17) if those assumptions are found to be incorrect?
I would also need to take into account the amount already implemented under the first CE.

The PM does not have authority to correct an error in an implemented CE, but nothing in NEC precludes the parties from mutually agreeing revised terms in a supplementary agreement. You should check that you are authorised to do so with the Employer.

Alternatively, the Contractor could notify a breach, you can accept and then issue assumptions