Hello,
you can not customize this type of entity. this is a system static entity.
As Tavok mentioned, this is system static entity and you really can't change it.
I have done something similar to this, which is a customized qualify lead process. Here are the steps to achieve it and hope it helps
1. Create a custom web resource html which replicates the original popup with you own customization such as adding/removing some fields. Put JS code to perform your customized resolve case process.
2. Create web resource JS to invoke the custom popup.
3. Update the Ribbon to override the oob resolve case to your own JS you created in Step 2.