Hi,
I checked both 11.5 and 11.6 UCCX versions and looks like the maximum predefined response character size is 1500 and cannot be modified. As a workaround, I would suggest creating two predefined responses of 1500 characters each and assign it to the same CSQ. The assigned CSQ will get displayed under the "Tags" field as shows below :
Thanks and Regards,
Deepak Nair