A CE is notified and from the accepted programme, it would be possible to carry out the work the work without delaying the Completion Date.
However, this would only possible if additional resources are deployed.
Can the PM insist that additional resources be deployed to carry out work in order to avoid time related costs?
The Contractor is obliged to obey an instruction from the PM which is given in accordance with the contract, which doesn’t include an instruction to implement acceleration, notwithstanding the procedure at clause 36.
Following discussion, the PM may instruct the submission of alternative quotations, or you could submit such a quotation without discussion, which includes positive measures to address the effects of delay which are at the risk of the Employer. If such a quotation is accepted by the PM, then this risk would pass to the Contractor to manage.
A Contractor should act competently and promptly to a compensation event (written) and also mitigate the effects practically (unwritten). If it is practically easy to get additional resources and work in parallel with other works then they should, rather than just saying they will do it at the end with their own labour.
A subtle point as well. In your question you actually mean it is possible to carry out the works without affecting “planned Completion” as that is what you are testing. If a compensation event affects “planned Completion” then you get to move Completion Date by the same amount.