A content management system using WordPress has been set up on an Amazon Elastic Kubernetes Service (EKS) instance. After a few weeks, you realise that the system is starting to reach its limits and needs to be scaled up as soon as possible. To carry out the upgrade, the content management system has to be shut down for a period of time. Although, this is NOT a good practise for businesses. Continuous service delivery and continuous system integration are preferred.

Propose a cloud-based solution which avoids the disruption such as shutdown completely? Elaborate on your cloud-based solution, its corresponding architecture and operation in detail.