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If you exceed your CPU and/or RAM resources your website is still going to be accessible but the load time will be longer because CPU and RAM are related to the read/write speed for your account. Also, this will cause a slower upload and download for files on your account. If you exceed the resources of your package, you need to review the following fist:
This should resolve the issue with the high resource consumption of your website on the server. However, if no further optimization is possible, you will have to consider a private Cloud VPS or Dedicated Server for your project. On it, you will have your own environment and you will be able to work on your website, without being limited to the resource amount you could use.