Can I make changes current activities once EOT is Granted due to Extra work

Dear All;

I have an approved baseline & now client is asking to add scope of work that was not initially include in the contract.

we have EOT of 30 days to accomodate these extra activities.

Can I change (delay) existing activities by 30 days also.

or

I have only right to show new scope in 30 days of EOT and keep existing schedule the same?

I also need some clause or reference to validate.

Thanks